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Risk Assessment for Floods Due to Precipitation Exceeding Drainage Capacity November 2006 Umut Karamahmut Faculty of Civil Engineering and Geosciences i i. Abstract Studies on flood risk modeling were concentrated on floods caused by breaches of dunes and levees. Another kind of flood which was not considered in risk calculations was floods due to precipitation exceeding drainage capacity of low lands. As a result of the increase in the extreme precipitation events due to climate change and increased land value, the risk due to this kind of floods increased considerably, and must be calculated. This study aims to investigate and improve current situation in risk assessment of floods due to rainfall exceeding capacity of the drainage system of polders. In order to achieve this, commercially available models were investigated to find out if any of them are capable of calculating risk for these floods. Research on existing models showed that none of these models were applicable for this problem. Calculation of risk for this kind of floods comes along with massive work load. In order to able to carry on these calculations the problem must be simplified by eliminating one o the parameters. In order to validate this simplification, correlation between two flood parameters namely, flood depth and flood duration were proved. Finally applicability of a risk analysis tool for this problem was investigated with a case study on Polder Berkel. Results showed that risk analysis methods were applicable to the case but some improvements were necessary. ii ii. Acknowledgments I would like to express my thanks to Elgard van Leeuwen and Olivier Hoes for their constant supervision and valuable comments through out my studies. I also would like to thank to Nick van de Giesen, Elgard van Leeuwen and Olivier Hoes for taking part in my graduation committee. I appreciate contributions of Colin Green and Edmund Penning-Rowsell from Flood Hazard Research Centre, Middlesex University, United Kingdom, Roy Leigh from Natural Hazards Research Center, Macquarie University, Australia and Duncan Faulkner from JBA Consulting – Engineers & Scientists and all WL|Delft Hydraulics employees who were always there to answer my questions and support me. The last but not the least I would like to thank to my family and friends, without their support none of this would be possible. Especially to my mother, for holding up to life. iii Table of Contents 1. Introduction:................................................................................................................ 1 1.1. Flooding ................................................................................................................... 1 1.2. Problem .................................................................................................................... 3 1.3. Objectives ................................................................................................................ 4 1.4. Report structure........................................................................................................ 5 2. Research on existing flood risk models ...................................................................... 6 2.1. Introduction.............................................................................................................. 6 2.2. Basics of flood risk estimation................................................................................. 7 2.3. Existing Flood Loss Estimation Models ................................................................ 10 2.4. Evaluation .............................................................................................................. 25 2.5. Conclusion ............................................................................................................. 27 3. Correlation of flood depth and duration for different soil types............................... 29 3.1. Introduction............................................................................................................ 29 3.2. Methodology .......................................................................................................... 30 3.3. Model Schematization ........................................................................................... 31 3.4. Model Data............................................................................................................. 32 3.5. Post processing of simulation results..................................................................... 37 3.6. Results.................................................................................................................... 41 3.7. Evaluation & Conclusion....................................................................................... 45 4. Case Study: Polder Berkel ........................................................................................ 46 4.1. Introduction............................................................................................................ 46 4.2. Polder Berkel ......................................................................................................... 47 4.3. WB21 Method........................................................................................................ 50 4.4. Risk Model............................................................................................................. 58 4.5. Case Discussion & Comparison............................................................................. 64 4.6. Conclusions............................................................................................................ 69 5. Conclusions & Recommendations............................................................................ 70 5.1. Conclusions............................................................................................................ 71 5.2. Recommendations.................................................................................................. 73 6. References................................................................................................................. 75 7. Appendix................................................................................................................... 77 iv List of Figures Figure 1-1 Inundation map of Netherlands without dikes, dunes and pumping stations... 1 Figure 2-1 Water Surface Profiles Plot............................................................................. 12 Figure 2-2Depth-Percent Damage Functions For Apartments ........................................ 13 Figure 2-3 Scale levels of damage evaluation .................................................................. 14 Figure 2-4Property Damages Output of MDSF................................................................ 18 Figure 2-5Components of FloodAUS............................................................................... 23 Figure 2-6 3-D representation of flood extend ................................................................. 24 Figure 3-1SOBEK Model Schematization........................................................................ 31 Figure 3-2Ernst Drainage Calculation Parameters ........................................................... 33 Figure 3-3Drainage Coefficients Input Screen ................................................................. 34 Figure 3-4Visual Basic script for determination of events ............................................... 38 Figure 3-5Output file view of the script ........................................................................... 39 Figure 3-6Depth – Duration graph for Sand Average (average) ...................................... 41 Figure 3-7Depth – Duration graph for Sand Average (maximum)................................... 42 Figure 3-8Trend lines of different soil types (average) .................................................... 43 Figure 3-9Trend lines of different soil types (maximum) ............................................... 43 Figure 4-1Sub-polders and target elevations .................................................................... 48 Figure 4-2Satellite Image of Polder Berkel ...................................................................... 49 Figure 4-3Damage Function for Greenhouses and Urban Areas...................................... 55 Figure 4-4SOBEK Model for Polder Berkel .................................................................... 56 Figure 4-5WB21 Script Output File View........................................................................ 57 Figure 4-6Digital Elevation Map Figure 4-7Water Compartments................... 59 Figure 4-8 Land Use Map ................................................................................................. 60 Figure 4-9Risk Model Damage Functions........................................................................ 61 Figure 4-10Hymstat Output .............................................................................................. 62 Figure 4-11Risk Map ........................................................................................................ 63 v List of Tables Table 2-1 Damage categories.............................................................................................. 8 Table 2-2 Inundation parameters ........................................................................................ 9 Table 2-3Stage-Damage relations for residential properties ............................................ 19 Table 2-4Damage categories for commercial properties .................................................. 20 Table 2-5Stage-Damage relations for commercial properties .......................................... 21 Table 2-6Coverage of existing flood loss estimation models........................................... 25 Table 3-1Unpaved node parameters ................................................................................. 32 Table 3-2Ernst coefficients for different soil types .......................................................... 35 Table 3-3Coefficient of Determination for different soil types ........................................ 44 Table 3-4Correlation Coefficient for different soil types ................................................. 44 Table 4-1Maximum damage per hectare for different land use........................................ 51 Table 4-2Workability coefficients for seasons and soil types for grassland .................... 52 Table 4-3Workability coefficients for seasons and soil types for agriculture .................. 53 Table 4-4Workability coefficients for high quality agriculture and horticulture ............. 54 Table 4-5Drowning coefficients ....................................................................................... 54 Table 4-6Risk calculated by Risk Model and WB21 method........................................... 65 Table 4-7Monetary Difference and Ratio between Risk Model and WB21 method........ 66 vi 1. Introduction: 1.1. Flooding The Netherlands, being located in delta of The Rhine, The Meuse and The Scheldt, has a long history in coping with floods. As a result of past water management practices, land reclamation and subsidence, higher percentage of The Netherlands lies on large flat plains under mean sea level. Thus they require both protection from sea and constant drainage of the excess water out of the polders. (See Figure 1.1) Figure 1-1 Inundation map of The Netherlands without dikes, dunes and pumping stations Source: Hoes, 2005 1 Studies on flood protection and flood damage modeling were mostly concentrated on the floods caused by breaches of dunes and levees since a flood resulting from these would be sudden and extensive and combined effects may be catastrophic but recently attention was also given to floods due to precipitation exceeding capacity of the drainage canals and pumping stations of polders. This kind of flood is neither life threatening nor as catastrophic as the floods due to breaches of dunes and levees but they might occur rather frequently resulting in substantial losses. (Hoes, 2005) Both total annual precipitation and extreme precipitation events are following an increasing trend especially in the last two decades. It is believed that this trend will continue due to climate change and further more floods events will be more frequent because of sea level rise and subsidence.(IPCC, 2001) Increase in frequency and magnitude of these events once again showed that regional rainfall induced floods can not always be prevented. On the other hand possible losses due to these events are also escalating because of increasing value of land and on going urbanization. In order to avoid these losses many water systems must be upgraded. Risk of flooding must be calculated in order to asses the feasibility of the measures taken to upgrade these systems. 2 1.2. Problem Commercially available models did not focus on this kind of floods but with current increase in risk these floods must also be covered. On the other hand risk estimation for this kind of floods is rather difficult. For risk assessments of river and sea floods in low lands, structures are assigned a failure probability then the risk can be determined by multiplying this probability with the possible damage that failure of this structure will cause. Total flood risk is the summation of risk values of all sections and structures. Not like river and sea floods, for a flood caused by precipitation exceeding drainage capacity, failure is not limited to one section or structure and also there is not only one failure probability for a section. Failure probability differs from frequent floods with small damages to low frequency floods with a higher damage and this probability distribution is dependent on elevation of each pixel. In other words both probability and damage are spatially distributed. This makes risk assessment much more difficult.(Hoes, 2005) Total risk for this kind of flood is summation of all multiplications of probability and damage. Calculation of rainfall induced flood risk has a vast workload due to the fact that probability of occurrence and damage in case of occurrence is spatially distributed. In order to be able to estimate the risk, this work load has to be reduced. In order to achieve this one of the parameters used in calculations can be excluded but this can be done only if the excluded parameter will be represented inclusively by the other parameters (ie. If there exists a correlation between them). 3 1.3. Objectives This study aims to investigate and improve current situation in determination of risk of floods in low lands due to rainfall exceeding drainage capacity. In order to achieve this, following objectives will be studied through out the study. - To figure out if any of the commercially available models are capable of solving this problem considering the different nature of rainfall induced floods in low lands. - To prove the correlation between flood depth and flood duration. This correlation is rather important because proof of such a correlation will allow us to eliminate one of these parameters, reducing the vast workload and enabling us to calculate risk. - To investigate the applicability of a new risk analysis tool for calculation of risk for rainfall induced regional floods in low lands. 4 1.4. Report structure The above mentioned objectives were addressed in different chapters as described below. In chapter two current practices and models in three countries namely as United Kingdom, United States and Australia were investigated in order to figure out if any of the commercially available models were capable of solving this problem. Existing models were not capable of carrying out this calculation. In the third chapter correlation between flood depth and duration was proved by simulating water levels for a long enough period for 12 most common soil types in Netherlands. In the fourth chapter a case study was carried out in order to investigate the applicability of a new risk analysis tool for calculation of risk for rainfall induced regional floods. Annual average risk calculated by this tool was compared with the risk value calculated by a traditional damage assessment method. Rationales behind risk calculation were investigated in order to reach a balance between workload and accuracy. The study was concluded and recommendations for further studies were given in chapter five. 5 2. Research on existing flood risk models 2.1. Introduction In this chapter applicability of existing flood risk models to the case of floods in low lands due to precipitation exceeding drainage capacity will be investigated by studying working principles of 6 models used in 3 countries. These models and countries are as follows. United States : - HAZUS - MH - HEC-FDA United Kingdom : - ESTDAM - MDSF Australia : - ANUFLOOD - FloodAUS Studies showed that current flood risk modeling practices in different countries are not applicable for modeling of flood risk due to high precipitation which exceeds the capacity of the drainage system. Reasons why they are not applicable will be mentioned further on. In following section basics of flood risk analysis and common practices will be mentioned. In third section an overview of the flood risk estimation methods used in different countries will be given. Evaluation of applicability of these methods to the case of concern will be carried out in forth section and conclusions will be given in fifth section. 6 2.2. Basics of flood risk estimation In this section, common practices used in different models thus different countries will be mentioned. In all of the models flood risk is defined as the sum of multiplication of damage in case of occurrence of events and probabilities that those events will occur. In order to calculate risk inundation maps with known occurrence probabilities were used. Flood damage and risk were categorized in different ways. These are as follows. 2.2.1. Type of flooding Damage and risk can be categorized according to the source of flooding. A flood might be caused by sea, river or precipitation. The source of flooding effects damage in various ways. For example a sea flood will have extra damage on agricultural fields due to salination. Also source of flooding changes calculation method for risk of flooding. 2.2.2. Categorization according to consequences In general there exists there different criteria to classify damages caused by natural disasters. First division is between tangible and intangible damages. Tangible damages are those which can be described in monetary units, thus they can be evaluated and compared. Damages to buildings or contents of buildings can be an example to tangible damages. Intangible damages are the ones which is difficult to describe in economic terms, for example physical and psychological traumas. Recently more studies are being carried out for quantification of intangible damages. An exemplary is “AnxietyProductivity and Income Interrelationship Approach” (API). This approach is explained in detail elsewhere (Lekuthai, Vongvisessomjai, 2001) 7 Another division is direct and indirect losses. Direct losses are caused by physical contact of flood water while indirect losses are caused through interruption and disruption of economic and social activities as a consequence of direct flood damages. (Dutta et al.,2001) Destruction of buildings is a direct damage while production loss is an indirect damage. Direct, indirect and tangible, intangible damages can further be divided as primary and secondary damages. The table below can be an example for the division of damages according to the above mentioned criteria. Table 2-1 Damage categories Category Direct Primary Tangible Capital Loss (houses, crops, cars, factory buildings) Indirect Production losses, income loss Secondary Induced Production losses outside the flood area, unemployment, migration, inflation Costs for relief aid Intangible Victims, ecosystems, pollution, monuments, culture loss Social disruption, emotional damage Emotional damage, damage to ecosystem outside the flood area Evacuation stress Source: K.M. de Bruijn, 2005, pg. 41. Ideally all these kinds of damages should be considered in estimations but in practice this is impossible. In most of the studies damages are restricted to primary tangible damages and part of the production losses by companies and agriculture. This is due to the complexity of calculating secondary tangible or intangible damages. These damages are introduced in bulk form by multiplying the primary tangible damage by a factor which is dependent to the properties of the region. 8 2.2.3. Effective parameters Adequate determination of flood parameters is also crucial for loss estimation. A list of inundation parameters is given in Table 2.2. Most important parameters are flow velocity, duration and depth of flow. For most cases only parameter used in models is the flow depth. This is an acceptable simplification since flood depth and duration are closely related to each other. In other words if the flood depth is high then it will take more time to drain the flood plain thus the flood duration will be longer. Table 2-2 Inundation parameters Inundation parameter Area Depth Duration Velocity Risk rate Time of occurrence Contaminations Salt / Sweetwater Relevance Determines which elements at risk will be affected Has the strongest influence on damage Influence on damages on building fabric Only high velocities will lead to increase in damage Influence on damage reducing effects of warning and evacuation Important on agricultural products Contaminations and loads may increase damage significantly Salt water can increase damages in coastal areas Source: Penning-Rowsell et al., 2005 Most of the models follow the unit loss approach for estimates. Unit loss model is based on unit by unit assessment of potential damage and summation of these possible damages gives the total expected damage. Success of loss estimation models mostly depends on the establishment of the relation of the damage with flood parameters. This is done with so called stage-damage functions which define the possible damage percentage for a given value of flood parameter. These functions are derived according to historical loss data, questionnaire or results of experiments. Potential damage for a given stage is found by multiplying the percentage corresponding to that stage value with the value of the structure. In common practice above mentioned principles are used in models but there exists some differences between methods and models developed in different countries. These methods, models and differences between them will be mentioned in next chapter. 9 2.3. Existing Flood Loss Estimation Models Different damage assessment models were developed in different countries. These models are mainly built for cost efficiency studies of flood mitigation measures or assessment of risk for insurance purposes. In this section different models used in United States, Australia and United Kingdom will be mentioned. 2.3.1. United States: In United States a variety of organizations are involved in damage assessment and prevention. As a result no standard method has been developed. (K. de Bruijn, 2001) There are two commonly used models, HEC-FDA and HAZUS-MH. 2.3.1.1. HAZUS-MH: The name of the model stands for “Hazard United States – Multiple Hazards”. HAZUS was initially developed for assessment of earthquake damages by Federal Emergency Management Agency (FEMA). Later FEMA released a newer version by which a variety of hazards, including floods, and their risk assessments may be investigated. HAZUS is a flexible program that allows performing the analysis on different levels depending on resources and analysis needs. Level 1 uses available hazard and inventory data provided by HAZUS-MH, limited additional data is required in this level. Level 2 analyses require local data which is readily available for most of the cases or can be converted to model requirements easily by Flood Information Tool (FIT, a built in function of the model for conversion of data). Level 3 involves adjustment of built in loss estimation models. 10 Loss estimate analysis can be run for three different analysis options. These options are; (1) multiple return periods of 10, 50, 100, 200 and 500 years, (2) a user defined single frequency or (3) annualized loss. For comparison of flood mitigation measures third option will be most adequate. (FEMA, 2004) Although the model gives a quick estimate of the possible damage, results will not be accurate enough unless the model is run on third level, which requires aggregation of detailed local data and adjustment of loss estimate models. 2.3.1.2. HEC-FDA: In United States, US Army Corps of Engineers (USACE) has nationwide responsibilities on water resources planning and management. (Dutta et al.,2001) Thus for flood mitigation measures USACE produced its own guidelines namely as the National Economic Development Procedures (USACE,1988) and The Hydrologic Engineering Center (HEC) designed the Hydrologic Engineering Center’s Flood Damage Analysis (HEC-FDA) program in order to assist risk-based analysis methods for flood damage reduction studies as required by USACE. HEC-FDA uses Monte Carlo simulation, a numerical model that computes the expected value of damage while explicitly accounting uncertainties in basic functions. It can quantify the uncertainty in discharge – frequency, stage – discharge, geotechnical levee failure and stage – damage functions and incorporate these into economic and performance analysis of alternative flood damage reduction plans. Evaluations are carried on in terms of expected annual damage equivalent annual damage or project performance. (USACE, 1998) 11 Model uses water surface profiles and depth damage functions for calculating damage and risk. Water surface profiles can be discharge or stage based. A data set must contain eight profiles. These are defined as 0.50, 0.20, 0.10, 0.04, 0.02, 0.01, 0.004 and 0.002 exceeding probability flood events. Profiles can be used for developing with or without project condition functions. They are also used to from stage-damage functions. An example plot of water surface profiles was given in Figure 2.1. (Burnham, 1997) Figure 2-1 Water Surface Profiles Plot Depth-percent damage functions can be assigned for each occupancy type. Program allows user to define three types of depth-damage functions namely as Structure, Content and Other. These functions can be calculated according to historical loss data, questionnaire or experimental results. Some depth-percentage damage functions used in a case is given below. (See Figure 2.2) The methodology adopted is very comprehensive for estimation of damage to urban buildings and to agriculture. However no specific methods have been developed for estimation of damage to lifeline systems and indirect losses such as interruption losses. (Dutta et al., 2001) 12 Figure 2-2Depth-Percent Damage Functions For Apartments (Left: structure, Right: Content) 2.3.2. United Kingdom: In United Kingdom it is mandatory to use a standard approach for flood damage assessment for local authorities which want the assistance of central government with flood mitigation measures. Flood Hazard Research Center (FHRC) in Middlesex University had been leading the studies for development of flood damage estimation methodologies on UK. (Dutta et al., 2001). FHRC published 4 manuals presenting results of their studies. The “Blue Manuel” (Penning-Rowsell and Chatterton, 1977) covers assessment techniques and provides a range of depth-damage data. The “Red Manuel” (Parker et al., 1987) provides depth-damage data and assessment methods for common indirect losses and direct losses except the residential losses were also covered in this manual. The “Yellow Manual” (Penning-Rowsell et al., 1992) covers the effects of coastal erosion and assessment of environmental effects of floods. Finally FHRC 13 published the “Multi-Coloured Manual” (Penning-Rowsell et al., 2003). This manual is called “Multi-Coloured” since it combines the techniques mentioned in previous manuals. It covers flood alleviation benefits, indirect benefits and coast protection and sea defense benefits in an improved and updated manner. In UK an object oriented hierarchical method is used for flood damage estimation. A methodology is selected according to size of the area under investigation and precision required from the study. Three different approaches were recommended according to size of area and precision namely as; macro scale, meso scale and micro scale damage evaluation (See Figure 2.3). Each method recommended for respective scale differs in terms of data requirements, damage categories considered, inundation characteristics needed, land use data, value assets, damage functions, damage calculation and presentation. (Penning-Rowsell et al.,2005) Size of Area under Investigation Accuracy local micro scale regional meso scale (inter-)national macro scale Effort, Costs/ Unit of Area Source: Meyer 2001, p. 30; Reese 2003, p. 54 Figure 2-3 Scale levels of damage evaluation 14 It can be observed that in United Kingdom damage functions published in the “MultiColoured Manuel” from FHRC build the basis of damage evaluation studies. For small scale project appraisals the full detail of the database is used. For meso and macro scales more aggregated damage functions are used. (Penning-Rowsell et al.,2005) This set provides synthetically derived depth-damage functions for 100 residential and more then 10 non-residential property types. For residential flats, first a definition and inventory of this standard property type is done. Secondly, for each of its typical building fabric and inventory components the monetary value is determined. Thirdly, expert assessors estimate the susceptibility of each item to inundation depth so depth-damage functions can be constructed. For non-residential properties surveys are carried out, in which responsible persons in each firm are asked about the value of assets at risk and susceptibility of these assets to inundation depth. From survey results average depth-damage curves per square meter of property are derived for different economic branches. (Penning Rowsell et al., 2003) These damage functions not only consider the inundation depth but also they consider duration of flooding (i.e. more or less than 12 hours), coastal flood or not (i.e. salt or fresh water), if a warning more than two hours is received. Two models used in United Kingdom will be mentioned briefly. 15 2.3.2.1. ESTDAM: ESTDAM non-GIS based model developed by FHRC. It is mostly used in micro scale studies for project appraisals. It applies a property by property approach and it is matched with the standard depth-damage data. It first calculates the depth of flooding in each individual property from the output of flood extent model. For each individual property it has the details of land use classification data. So once the depth of flooding in the property is determined it looks up the depth-damage function for relevant land use class and can calculate the flood damage at that individual property. (Penning-Rowsell E.C. et al., 1987) Depth-damage functions published in the “Multi-Coloured Manuel” are used to the full extend in this program. It also calculates the loss-probability curve and hence calculates the risk and present value of benefits. But it must be kept in mind that ESTDAM was developed in midseventies. Since the economic functions are not up to date, nowadays tendency is taking the event losses from ESTDAM output and calculate these values with more sophisticated, dedicated programs. 2.3.2.2. MDSF: MDSF stands for Modelling and Decision Support Framework. It was developed in 2001 to support Catchment Flood Management Planning by a consortium of organizations which was founded by Department for Environment Food and Rural Affairs (DEFRA) and the Environmental Agency, led by H R Wallingford and including Halcrow, the Centre for Ecology and Hydrology at Wallingford and the FHRC at Middlesex University. (Defra, 2003) 16 MDSF was designed as customized GIS tool to work with ArcView. MDSF is not a decision making tool and it does not contain a hydraulic model. It was designed as a decision support framework, providing common approaches and tools for assisting determination of flood management options at broad scale. It is particularly strong in assessment of the economic and social effects of flood management policies (Defra, 2003). As common practice in UK, it uses the depth-damage functions provided by the “MultiColoured Manual”. On the catchment level it uses only one sector average function for residential properties and ten for non-residential properties. Functionalities provided by the software can be listed as flows (Defra, 2004), - Facilitates for managing and viewing spatial data. - Assessment of flood extend and depth. - Calculation of economic damages due to flooding. - Calculation of social impacts due to flooding including the population in flood risk area and their social vulnerability. - Economic assessment of erosion losses. - Presentation of results for a range of Cases to assist the user in the selection of the preferred policy. Each case is a combination of climate scenario, land use scenario and flood management option. - Procedure for estimating uncertainty in the results. - Framework for comparing flood damages and social impacts as an aid to policy evaluation. - Archiving of cases. 17 Powerful visualization of results in GIS environment is a major advantage of the software since it makes the communication and comparison of the results much easier and more understandable for policy makers. A property damage map and tabulation is shown in figure 2.4. Figure 2-4Property Damages Output of MDSF 2.3.3. Australia: A recent research in Australia suggests that there is no standard approach for flood damage assessment in Australia. (Dutta et al., 2001) Nevertheless, Department of Natural Resources and Mines (NR&M) published “Guidance on the Assessment of Tangible Flood Damages” in September 2002. This guidance will be explained in the remainder of this section. 18 NR&M recommends adopting the stage-damage curves developed for ANUFLOOD. The curves for this flood damage model were developed for a range of building types and sizes. They cover residential buildings for a range of property size and commercial buildings for a range of contents and size. Flood damages can be estimated in 5 steps according to the guidance (NR&M, 2002). 1. Identify flood-affected properties and the likely height of inundation. Flood extend maps provides information about the locations of properties that might possibly be effected from a flood. In order to be able to use stage-damage curves an inundation depth must be estimated. This is done by simply subtracting ground height (site survey or existing maps) and floor level (building approval record) from the flood height (predicted by flood model). 2. Select appropriate stage-damage curves for determining potential direct damages. In this guidance there exist 3 curves for residential properties classified according to their sizes. Commercial properties are divided according to their size and branch of commerce. Details of these curves were given in Table 2.3, Table 2.4 and Table 2.5. Table 2-3Stage-Damage relations for residential properties Source: CRES, 1992, ANUFLOOD: A Field Guide, prepared by D.I. Smith and M.A. Greenaway. 3. Apply stage-damage curves to estimate potential direct damages from flooding. Application of stage-damage curves is simply finding the relevant stage-damage curve and interpolating the respective damage according to the inundation depth. 19 4. Estimate indirect losses. In common practice indirect losses are estimated as a percentage of direct losses. ANUFLOOD model uses 15% of direct losses for residential properties and 55% for commercial properties. 5. Calculate total (direct and indirect) damages. Total damage is summation of direct and indirect damages. Table 2-4Damage categories for commercial properties Source: CRES, 1992, ANUFLOOD: A Field Guide, prepared by D.I. Smith and M.A. Greenaway. 20 Table 2-5Stage-Damage relations for commercial properties Source: CRES, 1992, ANUFLOOD: A Field Guide, prepared by D.I. Smith and M.A. Greenaway. 21 For economic assessment of flood mitigation projects results must be given in terms of average annual damages (AAD). Calculation of AAD requires potential damage bills of a number of flood sizes with different occurrence intervals. AAD can be calculated in 4 steps. 1. Estimate potential damage costs from a range of flood sizes. 2. Plot graph of potential damages versus annual exceedance probability. 3. Calculate annual average damage costs from flooding. (i.e. the area under the damage vs. probability graph) 4. Calculate potential reduction in annual average damage from flood mitigation activities. Two models are distinguished in Australia. First was is ANUFLOOD, developed by Center for Resource and Environmental Studies (CRES) at Australian Natural University (ANU). Macquire Researc Ltd. purchuased the intellectual rights of ANUFLOOD on behalve of Natural Hazards Research Centre (NHRC) in order to modify it for insurance purposes and they release FloodAUS. Both ANUFLOOD and FloodAUS performs the above mentioned procedures. Both models will be mentioned briefly. 2.3.3.1 ANUFLOOD: ANUFLOOD was developed during 1980’s and early 1990’s by David Ingle Smith and Mark Greenaway. It is an interactive program designed to assess tangible urban flood damage. (Penning-Rowsell E.C. et al., 1987) 22 Input information includes building-by-building description of location, ground and floor heights, construction material, value, house size number of storey and so on. Flood frequency input to ANUFLOOD uses a listing of flood stages expressed as probabilities. Stage damage curves are provided for three residential properties with a further set of commercial property subdivided by size and susceptibility of contents to flood damage. Program also allows the user to input stage-damage curves. Inputs and processes of ANUFLOOD can be listed as follows. (Penning-Rowsell E.C. et al., 1987) 2.3.3.2 FloodAUS: FloodAUS is a GIS based risk rating tool developed by Risk Frontiers to estimate mainstream flood risk in urban areas on a per address basis. Model uses the following information to estimate flood risk: - Digital terrain models - Flood surface elevation information - Property street address databases Source: Risk Frontiers, 2002 Figure 2-5Components of FloodAUS 23 Information about extend and depth of flooding is achieved by combining the DTM and flood surface. Figure FFF shows inundated areas for a 100-year flood in New South Wales. Dark blue represents deep water and light blue shallow water. Source: Risk Frontiers, 2002 Figure 2-6 3-D representation of flood extend The main output is a database of street addresses, each with a flood risk rating. FloodAUS provides estimates of Average Recurrence Interval (ARI) of inundation at ground level, 1 meter above ground level and 2 meters above ground level (Risk Frontiers, 2002). 24 2.4. Evaluation In the section above flood risk assessment methods and models in different countries were investigated. It was observed that these methodologies vary largely in different countries. For example determination of infrastructure damages is covered in detail in the “Multi-Coloured Manual” in United Kingdom but in Australia infrastructure damage assessment seems to be limited while in United States it is not covered at all. In other terms in these countries depth-damage curves for rural areas are not considered. Components covered in different methodologies where tabulated in Table 2.6. Table 2-6Coverage of existing flood loss estimation models Damage Categories Urban Damage Residential Non-residential Rural Damage Crop damage Farmland Fishery Infrastructure System damage Service loss Business Loss Environmental Damage United States United Kingdom detail detail detail detail rough rough detail detail none detail none detail none detail detail detail none detail Australia detail detail rough none detail rough rough detail none When risk estimation models were observed it was noted that all models use unit loss model. In other words they calculate the possible damage on a property-by-property basis. Risk is calculated in all models by finding the possible damage for different flood magnitudes and then weighting them with occurrence probability of respective floods. Possible damages were found either by using absolute depth-damage curves or using relative depth-damage curves and multiplying the damage percentages with the value of assets. 25 It was also observed that all of the damage models were mainly developed for urban damages. Rural damage functions were not considered in so much detail. In cases where crop damage was considered, damage functions did not consider effects of high groundwater levels. In other words depth-damage functions were plotted starting from ground level. But in real life effects of high groundwater levels on crop damage are known and must not be neglected. All above mentioned models were developed for river and sea floods. Calculation of risk for these kinds of floods differs from calculation of risk for floods occurring due to precipitation exceeding drainage capacity. While assessing risk for sea and river floods, structures are assigned a failure probability and risk is calculated as the product of this probability and possible damage that will be caused if the structure fails. In floods due to precipitation exceeding drainage capacity failure is not limited with one structure and failure probability is not constant. Failure might occur frequently with small damage and with a high damage but with lower frequency. Thus flood damage must be calculated over Probability-Density function. Also probability depends on elevation of each pixel and it is spatially distributed. Above mentioned models are not capable of assessing risk when both probability and possible damage are spatially distributed. 26 2.5. Conclusion Common practices in flood risk assessment in different countries and different flood risk models were investigated in order to find if any of these existent models are applicable to the problem of assessment of flood damage due to precipitation exceeding drainage capacity. The following conclusions were drawn. 1- All of the models studied were developed for floods caused by breaches of dunes and levees and were not able to calculate risk for floods caused by precipitation exceeding drainage capacity due to flowing reasons. - These models calculate damage for several inundation maps with known probabilities. But such a match of probability and inundation map for rainfall induced floods in low lands is not possible. - For this kind of floods failure is not limited to one section. Meaning, failure probability differs from frequent floods with small damages to low frequency floods with higher damage. - Probability is also dependent on the elevation of the pixel. As a result probability will be spatially distributed. Current models are not capable of calculating risk for spatially distributed probability functions. - Existing models do not cover effects of high ground water levels. 27 2- A new model must be developed that will be capable of handling the calculations due to the spatially distributed nature of probability and damage data. A GIS based model would be appropriate for this case. Probability and damage functions can be modeled by two separate grid layers. This way risk can be calculated by unit loss approach in terms of grid-by-grid consideration of risk. 3- Effects of high groundwater levels must be included in damage functions. As current models were developed mostly for urban damage, these effects were ignored. But for this kind of floods rural damage has a higher importance and effects of high groundwater levels can not be ignored. 28 3. Correlation of flood depth and duration for different soil types 3.1. Introduction As mentioned earlier, risk calculation for floods due to rainfall exceeding drainage capacity differs from river and sea floods. In the second one failure probability is constant but in the first case failure might occur frequently with small damage or less frequently but with a higher damage. As a result of this risk must be calculated for all the points on the probability distribution function of water levels. This means an enormous work load for calculation of risk. Thus any simplifications that will decrease this work load have great importance for such a risk model to work efficiently. Most important parameters for damage calculations in risk models are flood depth and flood duration. If these parameters can be replaced by one parameter the work load will reduce significantly making it possible to calculate the risk. In this chapter, correlation between flood depth and duration will be proved. As a result of this correlation flood depth can be used solely, while effect of duration will be covered inclusively. Relation between these parameters is dependent on drainage properties of the soil. In order to include effects of soil properties, 12 soil types were investigated. 29 3.2. Methodology Flood depth can be used as an indicative parameter. This is an acceptable assumption since flood duration is closely related to flood depth. In other words, if the flood depth is high then it will take more time to drain the flood plain, thus flood duration will be longer. At this section of the study validity of this assumption was investigated. In order to verify this assumption groundwater levels were simulated for a long enough time period that would enable the researcher to comment statistically on the results. These simulations were carried out with SOBEK Rainfall – Runoff Module for 12 most common soil types in Netherlands. Results were investigated statistically in means of RSquare and coefficient of correlation. 30 3.3. Model Schematization A simple model was built in SOBEK which will be capable of simulating the groundwater levels. This model consists of one unpaved node connected to an open water node and two pumps combining this node to boundary nodes in a way that will model the drainage system. Figure 3-1SOBEK Model Schematization In this model, precipitation falling on unpaved node is transferred to the open water node and drained further by downstream pump. Drainage capacity of the polder system was modeled by the capacity of the downstream pump. On the other hand upstream pump and upstream boundary node assures that open water elevation is kept on target level. (i.e. In case of drought water level is brought back to target level by pumping water in to the open water node) In the model unsaturated zone was simulated by using CAPSIM, which means that the storage coefficient used is calculated according to the actual groundwater level through out the simulation period. An hourly rainfall series of 333 years and a daily evaporation series for the same time period were used. Such a long simulation time gives enough events to judge on statistically. 31 3.4. Model Data While setting up the model attention was given to input data in a way that the model will be able to reflect the real world situation in the best way possible. In order to achieve this, input data was determined by using previous studies, values used in common practice and expert advice. In this part, input data used in the simulations were given for every node. 3.3.1. Unpaved Node: An unpaved node of 100 ha was used as a representative land. Vegetation was chosen as grass in order to avoid interference of vegetation in groundwater calculations. Parameters used are explained in detail below and listed in TABLE 3.1. Table 3-1Unpaved node parameters Parameter Area Ground Water Thickness Surface Level On Land Storage (max) Infiltration Capacity Value 100 ha 5m 0m 5 mm * area 20 mm/hr Storage coefficient determines the capacity of soil to store water before surface runoff occurs. Surface runoff starts when the precipitation is greater than the sum of maximum storage and infiltration capacity of the soil. In this simulation storage coefficient was chosen as 5 (mm * area). This value was determined by investigating previously used models. Infiltration capacity is the amount of water that can be infiltrated per unit area in unit time. In case that infiltration capacity is exceeded, water will be stored on land. In this simulation infiltration capacity was used as 20 mm/hr. This value was determined by investigating previously used models. 32 Drainage resistance is one of the most important parameters in groundwater level modeling. Groundwater outflow is calculated by using groundwater level, drainage resistance values, soil storage coefficients and downstream water level. d q Figure 3-2Ernst Drainage Calculation Parameters Ernst formula was chosen among the drainage calculation formulas since it is more convenient to use Ernst when the calculations in the unsaturated zone are carried out by CAPSIM. Ernst equation follows as; q = dH/ γ .f Where: q = drainage [m/d] dH = difference between groundwater level and drainage basis [m] γ = drainage resistance [d] f = factor depending on the shape of the groundwater table [-] (Ernst, 1978) 33 Figure 3-3Drainage Coefficients Input Screen Ernst values used in the model were determined with help of expert advice on subject for different soil types. Values used are given in TABLE 3.2. 34 Table 3-2Ernst coefficients for different soil types Soil Type Sand Maximum Peat Maximum Clay Maximum Peat Average Sand Average Silt Maximum Peat Minimum Clay Average Sand Minimum Silt Average Clay Minimum Silt Minimum Ernst Coefficient 50 10 20 20 20 50 10 20 50 20 20 50 3.3.2. Open Water Node: A constant area of 5 ha was used as open water node. This area was again determined according to regulations and previously carried out studies. Bottom level was determined as “datum – 2m”. In this case bottom level does not have any importance because the upstream pump will avoid an extensive decrease in the open water level by pumping in water from the upstream boundary node. Target level of the open water node was set to “datum – 1m”. 3.3.3. Pumps: Upstream pump station functions in a way that will keep the open water level at target value at times when rainfall is not encountered for a long period. This reflects the real world situation, since in periods with out rainfall, decrease of groundwater level in agricultural areas are prevented by controlling the open water level in the area by pumping in water. On the other hand it does not have a direct impact on the aim of this study. The study aims to model the drainage properties of soils under floods. If the 35 groundwater level is brought back to target level in case of drought, this will only increase the number of events during the simulation period, which will make the results statistically sounder. The upstream pump works as an inlet and checks downstream water levels for operation. Downstream pump station models the drainage system. It functions as a normal pump and checks upstream water levels. If the target value is exceed it starts operating. In order to avoid any lag, operation rules of the pump was set in a way that it would start operation if the deviation from target level is 1cm. This is not the case in real world operations due to the fact that such a management will increase operation costs. But since the aim is modeling of the soil, this is an acceptable application in the model. Pump capacity used in the model was 6.94m2/min. This value was determined as the mean value of pumps that were used in previous studies. 3.3.4. Boundary nodes: Boundary nodes were set in order to isolate the model. In other words with the help of boundary nodes it was made sure that there will always be enough water in the upstream to be used in case of drought and the downstream pump will always be able to pump out the maximum capacity of the pump. 36 3.5. Post processing of simulation results The aim of this study was obtaining a series of flood depth and flood duration parameters and observing them statistically in order to prove the correlation between these parameters. In order to obtain these series following processes were carried out. In order to begin analysis parameters had to be defined first. Definitions used were as follows. An event was defined as water level exceeding a given threshold. In this study the threshold was defined as “datum - .70m”, in other words 30cm above the target level. Flood duration was defined as the time between the first time that the water level exceeds the threshold and the time when the water level goes below the threshold. Two parameters were defined for flood depth, namely as “average depth” and “maximum depth”. Maximum depth was defined as the flood depth at the time when the water level reaches its highest value within an event while average depth was defined as the mean value of flood depth through out the entire event duration. Once the model was run, results were recorded to a history (.his) file. This history file included hourly values of unpaved node parameters for 333 years. Since the simulation period was excessively large, it was not possible to work further on these history files due to large file sizes up to 1.5 gigabyte. In order to be able to process, groundwater depth data were exported to tab separated text (.txt) files. These files were containing water level values for almost 3 million time steps. A script was written in visual basic in order to pick events within this large text file. The script used hourly water levels as input and recorded another text file which involves event duration, maximum depth and average depth parameters for every single event and a summary of entire simulation period at the end of the file. (I.e. Number of events, total duration above threshold, total simulation period) The script used is given in figure 3.4 and an exemplary output file view is given in figure 3.5. 37 Figure 3-4Visual Basic script for determination of events 38 Figure 3-5Output file view of the script Results in this file were plotted as two series, namely as maximum and average. Series “Maximum” indicates the duration and corresponding maximum groundwater level for each event. While series “Average” indicates the duration of the event and the mean value of groundwater level within that event. Further on statistical operations were carried out on these data sets in order to observe the correlation between these two parameters. First a trend line was calculated for each series. In order to be able to observe the correlation coefficient, trend line was chosen to be linear, which can be represented by the equation: y = (m*x) + b, and can be calculated by least squares fit method. Then coefficient of determination (i.e. R square) and correlation coefficient was calculated for each series. 39 Coefficient of determination (R2) is the proportion of a sample variance of a response variable that is "explained" by the predictor variables when a linear regression is done. In other words it is the proportion of the variability in one series, it is a measure of the quality of fit. 100% R-square means perfect predictability. The formula for R2 is where, ESS = explained sum of squares, RSS = residual sum of squares, and TSS = total sum of squares. Correlation coefficient (r), indicates the strength and direction of a linear relationship between two random variables. In general statistical usage, correlation refers to the departure of two variables from independence. The correlation coefficient will vary from -1.0 to 1.0. -1.0 indicates perfect negative correlation, and 1.0 indicates perfect positive correlation. If there is only one predictor variable than correlation coefficient can be calculated as the square root of coefficient of determination. r = R2 40 3.6. Results Above mentioned operations were carried out for 12 different soil types. After the post process of simulations flood depth – flood duration graphs were plotted. Examples of these graphs for average and maximum values can ve observed in figure 3.6 and figure 3.7 respectively. Sand Average - Average 0 0 50 100 150 200 250 300 -0.1 -0.2 Average Linear (Average) Depth (m) -0.3 y = 0.0009x - 0.6829 2 R = 0.8016 -0.4 -0.5 -0.6 -0.7 -0.8 Duration (h) Figure 3-6Depth – Duration graph for Sand Average (average) 41 Sand Average - Maximum 0.6 0.4 y = 0.0041x - 0.6816 2 R = 0.7691 Depth (m) 0.2 0 0 50 100 150 200 250 300 -0.2 Maximum Linear (Maximum) -0.4 -0.6 -0.8 Duration (h) Figure 3-7Depth – Duration graph for Sand Average (maximum) Linear trend lines were calculated by least square fit method for each soil type. Trend lines for average and maximum flood height values for different soil types are shown in Figure 3.8 and Figure 3.9. 42 Depth - Duration Average 0.6 Silt Average 0.4 Clay Minimum Clay Maximum Clay Average Peat Average Depth (m) 0.2 0 0 100 200 300 400 500 Peat Minimum600 Peat Maximum Silt Maximum -0.2 Sand Average Sand Maximum Silt Minimum Sand Minimum -0.4 -0.6 -0.8 Duration (h) Figure 3-8Trend lines of different soil types (average) Depth - Duration Maximum 3 Silt Average 2.5 Clay Minimum Clay Average Clay Maximum Peat Average 2 Peat Minimum Depth (m) 1.5 Peat Maximum Sand Average 1 Silt Maximum Sand Minimum Sand Maximum Silt Minimum 0.5 0 0 100 200 300 400 500 600 -0.5 -1 Duration (h) Figure 3-9Trend lines of different soil types (maximum) 43 Then coefficient of determination was determined for every different soil type. Resulting R-square values are given in the table 3.3 for average and maximum flood depth cases. Table 3-3Coefficient of Determination for different soil types Soil Type Peat Minimum Silt Average Clay Minimum Clay Average Clay Maximum Peat Average Silt Maximum Sand Maximum Silt Minimum Sand Minimum Peat Maximum Sand Average R^2 (Average) R^2 (Maximum) 0.359 0.361 0.450 0.482 0.571 0.623 0.707 0.724 0.724 0.735 0.748 0.802 0.425 0.377 0.431 0.441 0.495 0.522 0.686 0.704 0.706 0.718 0.692 0.769 Correlation coefficient was calculated as square root of coefficient of determination. Resulting r values are given in the table 3.4. Table 3-4Correlation Coefficient for different soil types Soil Type Peat Minimum Silt Average Clay Minimum Clay Average Clay Maximum Peat Average Silt Maximum Sand Maximum Silt Minimum Sand Minimum Peat Maximum Sand Average Correlation Coefficient (Average) Correlation Coefficient (Maximum) 0.60 0.60 0.67 0.69 0.76 0.79 0.84 0.85 0.85 0.86 0.86 0.90 0.65 0.61 0.66 0.66 0.70 0.72 0.83 0.84 0.84 0.85 0.83 0.88 44 3.7. Evaluation & Conclusion In this section drainage characteristics of 12 most common soil types in Netherlands were simulated. Main aim of this simulation was to see the correlation between flood depth and flood duration. Following conclusions were drawn from the simulations. 1- Correlation between flood depth and flood duration was proved. Thus it will be an acceptable assumption to disregard flood duration and use flood depth as an indicative parameter which will cover both coefficients. This will decrease the computational workload significantly. Correlation coefficient was noted to have an average of 0.77. The lowest value was 0.60 for peat minimum and silt average, while the highest value reaches to 0.90 for sand average. This value represents a strong positive correlation between flood depth and flood duration. 2- Trend lines for depth – duration relation was created from simulation results. It was observed that trendlines for clay was steeper than the ones for sand. This was an expected result due to the differences in permeability and storage coefficient. Flood depth tends to increase faster, reaches higher values, and remains high for a longer period in clay. While in sand, increse in flood depth is rather slowly and drainage is faster compared to clay. This explains the differences in slopes of trend lines. 3- Coefficient of determination was noted to decrease with increasing trend line slope. This is due to two main reasons. A lower trend line slope means faster and rather simple drainage. But in a steeper trend line, drainage is rather slow and other parameters like horizontal flow or effects of consequent rainfall events make it harder to be modeled linearly. Second reason is statistical. With the increasing slope of trend line number of events will increase. Thus with more events, number of deviations from the trend line also increases. 45 4. Case Study: Polder Berkel 4.1. Introduction A case study was carried out in order to investigate the applicability of a new risk analysis tool to floods due to precipitation exceeding drainage capacity. For this purpose the risk analysis tool that works on GIS basis using land use data, digital elevation model and probability density function of water levels was used to calculate the risk in the case study area. The risk calculated by the above mentioned risk analysis tool was compared with risk calculated by the risk calculated by another method namely as WB21. (Abbreviation for Waterbeheer 21st) As a matter of fact WB21 is not a risk model. It is rather a method for damage calculation for single events. But a risk value was obtained by summing up damage for every single event in a long enough period and dividing this damage sum to the simulation period. It must be noted that this case study does not aim to show the correlation between flood depth and duration which was proved in previous chapter since there exist many other parameters that effect the calculations within each model. But it must be also noted that the risk analysis tool used calculates the risk according to the fact that these two parameters are correlated. Further detail on both models will be given below. This chapter starts with brief introduction about the study area: Polder Berkel, follows with descriptions of both methods, comparison of results obtained and concludes with comparison and discussion of case study outcomes. 46 4.2. Polder Berkel The case study was carried out in Polder Berkel. The main reason for selecting this area as the case study area was the accessibility of meteorological data and rainfall-runoff model. In this section general information about the case study area will be provided. Polder Berkel lies between Rotterdam and Zoetermeer and covers an area of 2.052 ha. It lies within the borders of Berkel and Rodenrijs and Pijnacker-Nootdorp municipalities. The polder is divided into 12 sub-polders with 7 different target levels. The area is drained by three main drains to Binnenboezem. Sub-polders within the polder are named as follows, 1. Bergboezem 2. Meerpolder 3. Nieuwe droogmaking 4. Nieuwe Rodenrijsche droogmakerij 5. Noordpolder 6. Oostmeerpolder 7. Oudeland 8. Oude Leede 9. Voorafsche polder 10. Westpolder 11. Zuidpolder 12. Zuidpolder Rodenrijs Water level within the polder varies from -1.5m + NAP (abbreviation for Normaal Amsterdams Peil, i.e. Normal Amsterdam Water Level) in the middle parts of the Oudeland and -5.85m + NAP in the Zuidpolder. Sub-polders Oudeland and Voorafsche Polder are relatively higher within the main polder with an average level of -2.7m + NAP. On the other hand the Bergboezem, Westpolder and Zuidpolder are the lowest areas in the case area with an average elevation of -5.1m +NAP. A general view of the sub-polders and target elevations for summer and winter season is given in Figure 4.1. 47 Source: TAUW, 2002 Figure 4-1Sub-polders and target elevations 48 Prevailing soil type in the polder is clay. The polder is mostly covered with grass and agriculture. Percentage of grass and agricultural areas reaches to 64% while green houses cover 14% of the total area. 14% of the polder is used as urban. This distribution can be observed from the satellite image in Figure 4.2. Figure 4-2Satellite Image of Polder Berkel 49 4.3. WB21 Method This method had been presented for modeling damage due to high groundwater levels. Main reason of this damage is the fact that high ground water levels cause anaerobic conditions in the root zone and this leads to drowning of the crop. Other effects of high groundwater level on crop productivity are as follows: - Growing season for crops is shortened due to decreased yield and low temperature. - Fine soil particles form a crust layer. - Due to denitrification, nutrients that feed the crops are lost. - With high groundwater brackish or salt water can reach to root zone. The proposed model uses the general formula given below for damage calculations. D = f (h, âˆ†t ) * Dmax Where; D = damage per hectare f (h, âˆ†t ) = damage function dependent of depth and duration Dmax = maximum damage Damage functions and maximum damage amounts are depended on land use. This method uses 5 different land use form. Maximum damage amounts for different land use forms are given in Table 4.1. These amounts were calculated by Agriculture Economic Institute (Landbouw Economisch Instituut, LEI) as the average gross real turnover by hectare. 50 Table 4-1Maximum damage per hectare for different land use Land Use Damage Function Parameters Maximum Damage Grass Season 900 €/ha Agriculture Season, workability, drowning 3.600 €/ha High quality agriculture and Season, workability, drowning 18.000 €/ha horticulture Greenhouses Depth or duration 230.000 €/ha Urban Depth 2.300.000 €/ha Since agricultural damage is highly dependent on the time when the flood took place, different coefficients were defined for all four seasons. Damage due to workability is taken into account by a coefficient called sum of overshootings (SOW) of the critical groundwater elevation. Unit of this coefficient is cm*day. It is calculated by multiplying the overshooting with the duration. For calculating damage due to drowning, quadratic sum of overshootings (SKOW) is used. This is expressed as cm2*day. This is calculated by multiplying square of the overshooting with duration. The reason for using quadratic sum is to model the non-linear character of drowning damage. Four different damage functions are given for grass, agriculture, greenhouse, and urban. These functions are given in detail below. 51 4.3.1. Grass Damage Damage in grass land is mainly due to workability condition thus it is dependent on soil type and season. In this method, this differentiation is made by a coefficient called workability coefficient for grass land. Values of this coefficient are given in Table 4.2. Damage function for grass land is given as follows. f (h, âˆ†t ) = c 0 (t ) * SOWcd Where; c0 (t ) = workability coefficient for grass land (cm-1*d-1) SOWcd = sum of overshootings for given critical depth (cm*d) Table 4-2Workability coefficients for seasons and soil types for grassland Season (cm-1*d-1) (cm-1*d-1) (cm-1*d-1) Spring 20*10-5 10*10-5 5*10-5 Summer 26*10-5 17*10-5 17*10-5 Autumn 6*10-5 8*10-5 8*10-5 Winter 0 0 0 Critical Depth (cm) 20 40 75 4.3.2. Agriculture and Horticulture Damage Damage on agriculture is mostly dependent on the drowning of plants. Damage function is defined in a way that water level exceeding the root zone for three days causes complete loss of the crop. (Bolt et.al., 2000). Further on damage function is defined as the maximum of the damage due to workability and damage due to drowning. And it must be kept in mind that it can not be greater then 1 since damage function equal to 1 means 100% damage and a higher damage is not possible. 52 f (h, âˆ†t ) = max(c1 (t ) * SOWcd , c 2 (t ) * SKOWrz ) Where; c1 (t ) = workability coefficient (cm-1*d-1) SOWcd = sum of overshootings for given critical depth (cm*d) c 2 (t ) = drowning coefficient (cm-2*d-1) SKOWrz = sum of overshootings for given root zone (cm2*d) Coefficients to be used in the above formula are given in tables below. Differentiation for this coefficient was made with respect to seasons and soil types. Table 4.3 gives the workability coefficient for agriculture. Workability coefficient for high quality agriculture and horticulture is given in Table 4.4 and drowning coefficients are given in Table 4.5. Table 4-3Workability coefficients for seasons and soil types for agriculture Season Sand (cm- (cm-1*d-1) 1 (cm-1*d-1) (cm-1*d-1) (cm-1*d-1) *d-1) Spring 8*10-5 9*10-5 8*10-5 9*10-5 10*10-5 Summer 14*10-5 15*10-5 14*10-5 16*10-5 16*10-5 Autumn 7*10-5 7*10-5 7*10-5 8*10-5 8*10-5 Winter 0 0 0 0 0 Critical Depth (cm) 85 120 150 120 140 53 Table 4-4Workability coefficients for high quality agriculture and horticulture Sand (cm- (cm-1*d-1) Season 1 (cm-1*d-1) (cm-1*d-1) (cm-1*d-1) *d-1) Spring 14*10-5 14*10-5 14*10-5 16*10-5 16*10-5 Summer 24*10-5 24*10-5 23*10-5 27*10-5 27*10-5 Autumn 11*10-5 12*10-5 11*10-5 13*10-5 13*10-5 Winter 0 0 0 0 0 Critical Depth (cm) 85 120 150 120 140 (cm-2*d-1) (cm-2*d-1) (cm-2*d-1) (cm-2*d-1) 21*10-5 21*10-5 7*10-5 5*10-5 Table 4-5Drowning coefficients (cm-2*d-1) Season Spring, Summer, 21*10-5 Autumn Winter 0 0 0 0 0 Root Zone Depth 40 40 40 70 80 4.3.3. Greenhouses Damage In greenhouses high groundwater levels do not causes damage. In this case damage is caused by inundation. Two different damage functions were defined for greenhouses. First function is dependent on inundation depth while the second one is dependent on inundation duration. Damage functions for greenhouses are as follows. f (h) = min(0.2 + 1.6 * h,1) f (âˆ†t ) = min(0.5 + 0.06 * âˆ†t 2 ,1) Where; h = inundation depth (m) âˆ†t = inundation duration (d) 54 4.3.4. Urban Damage In this method urban damage is modeled according to the depth damage function given below. (See Figure 4.3) f (h) = min(0.01 + h,1) Where; h = inundation depth (m) Damage Functions 100 90 Damage percentage (%) 80 70 60 Urban Greenhouses 50 40 30 20 10 0 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Inundation depth (m) Figure 4-3Damage Function for Greenhouses and Urban Areas 4.3.5. Simulation and Risk Calculation For calculation of risk water levels within the polder had to be simulated for both methods. This simulation was carried out in SOBEK Rainfall-Runoff module. Model used for this simulation can be seen in Figure 4.4. 55 Figure 4-4SOBEK Model for Polder Berkel This simulation was run for 100 year long time period and groundwater and open water elevations were recorded for this period. Since the file size of these records were extensively large, these files were converted to tab separated text files, making it possible to further process this data. As it was mentioned earlier WB21 method is capable of calculating damage per event. In order to be able to calculate a risk value with this method, damage caused by all events within a period had to be calculated one by one and the yearly average of these damages would be the annual average risk value calculated with this method. Time period must be chosen long enough that this definition of annual average risk will be valid. In this study a 100-years period was chosen. 56 In order to carry on above mentioned calculations a script was compiled. This script takes groundwater levels as input and calculates annual average risk for each water compartment. This script takes land use, season, duration and depth into account as it was mentioned in the definition of WB21 method. Further on this script provides statistical information which will enable the user to judge on and compare outcomes. Following information was provided in the output file of the script; number of events in each season, duration of events in each season, number and damage function sum of events due to workability, number and damage function sum of events due to drowning, total duration above target level, total simulation period, total damage function and damage for grass and agriculture, total damage and annual risk. A view of output file can be seen in Figure 4.5. Figure 4-5WB21 Script Output File View 57 4.4. Risk Model The second model used in this study was a GIS based risk model. This model takes various data as input and calculates the annual average risk accordingly. Input files for this model can be categorized into two as, GIS data and other data. - GIS Data (maps in asci file format) - Digital Elevation Map (DEM) - Water compartments - Land use map - Other Input Data (data in comma separated value (csv) file format) - Target levels for water compartments - Damage functions and maximum damage values - Probability density functions for open water levels In order to run this model a digital elevation map of 25m X 25m was used. This map can be seen in Figure 4.6. In order to assess damage for sub-polders with different target elevations, water compartments were defined. These compartments were defined according to the unpaved nodes in the SOBEK model. A detailed presentation of these water compartments can be observed in Figure 4.7. 58 Figure 4-6Digital Elevation Map Figure 4-7Water Compartments Land use data was provided by a 25m X 25m land use file which consists of 16 major land use types. This land use map can be seen in Figure 4.8. 59 Figure 4-8 Land Use Map 60 Target level values for each compartment were defined in a csv file. Target values were calculated in a way that results from two methods will be comparable. In order to achieve this, target levels were set for every water compartment to mean elevation of the water compartment minus root zone depth. Maximum damage values and damage functions for different land use types were entered in another csv file. Damage functions used in this study can be observed from Figure 4.9. (Hoes, 2005) Damage Functions 100 90 Crops Grass Urban Damage percentage (%) 80 70 60 50 40 30 20 10 0 -50 -40 -30 -20 -10 0 10 20 30 40 Inundation depth (cm) Figure 4-9Risk Model Damage Functions Final input file used for this model was the file containing probability-density functions for each water compartment. These functions were calculated by using a statistical analysis program namely, Hymstat by considering 100 year long open water simulation results. Hymstat output graph can be observed in Figure 4.10. 61 Gumbel Distribution Location: 402 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 -5.4 -5.45 0.1 - 0.2 - - - - - -0.5 - - - - - - - 0.8 - - - 0.9 -- - -0.95 - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.35 Figure 4-10Hymstat Output Risk model creates two out files. First one is a csv file containing damage values for each water compartment. The second output is a risk map in the form of an Asci file. This file was converted to raster by using Arc Catalog. The raster form provides more user friendly visualization of the risk values. Resulting risk map can be observed in Figure 4.11. 62 Figure 4-11Risk Map 63 4.5. Case Discussion & Comparison Two models were run separately and resulting annual average risk values were compared. Annual average risk calculated by the risk model was 32055 € while the one calculated by the WB21 method was 33268 €. These two values represent almost a perfect match. The difference in between these numbers is 3.6%. When the results for each water compartment were investigated separately, it was noted that the perfect match mentioned above was not the case. It was rather a coincidence. Differences between risk values were observed in some of the water compartments. Risk values of all water compartments calculated by both methods can be observed in Table 4.6. 64 Table 4-6Risk calculated by Risk Model and WB21 method Water Compartment Number 306 312 317 322 325 330 336 337 344 346 352 359 364 367 373 377 383 385 389 395 399 402 407 411 414 419 423 427 430 434 Risk in € calculated by Risk Model 200 81 5 146 1 7 0 5 54 0 2 0 5 0 18 22 190 1031 2719 357 1309 13 4275 11353 1785 34 144 179 531 7587 WB21 Method 205 33 0 7 0 0 0 0 6178 0 594 8 692 0 84 997 81 5793 173 109 2800 77 3667 7972 280 1018 467 104 0 1930 Table 4.7 provides information about the extent of difference between two results. In this table monetary difference and ratio between two models were given for every water compartment. 65 Table 4-7Monetary Difference and Ratio between Risk Model and WB21 method Water Compartment Number 306 312 317 322 325 330 336 337 344 346 352 359 364 367 373 377 383 385 389 395 399 402 407 411 414 419 423 427 430 434 Monetary Difference (€) (RM – WB21) -5 49 5 139 1 7 0 5 -6124 0 -592 -8 -686 0 -67 -975 109 -4762 2546 248 -1490 -64 609 3382 1506 -984 -322 75 531 5657 Ratio (greater/smaller) 1.03 2.49 --20.34 --------113.41 --260.59 --131.24 --4.77 46.19 2.35 5.62 15.68 3.28 2.14 6.06 1.17 1.42 6.38 29.81 3.23 1.72 --3.93 There exist many differences between the two methodologies used. Considering these differences, it would not be reasonable to expect same results from both models. In the remainder of this case study, water compartments with significantly different risk values were investigated in order to find out the reasons of these distinct values. This investigation was carried out on various grounds and some rationales behind these differences were found. Investigated parameters were effects of season of occurrence of events, elevation differences within water compartments and land use data in a water compartment. These parameters will be mentioned in detail below. 66 4.5.1. Season of occurrence of events, Season of occurrence of events data was derived from the outcomes of the script for WB21 method. It was observed that water compartments with more events occurring in the winter season tend to give higher risk values for the Risk Model case. The main reason behind this is the fact that WB21 considers occurring time of events and damage function for events occurring in winter is predefined as zero. Thus no risk is introduced due to these events. While in the risk model no distinction between events occurring in winter and events occurring in growth season of crops was made. While preparing water level probability functions for Risk Model winter water levels were also considered. This leaded to higher probability of occurrence and thus higher risk. 4.5.2. Elevation differences within a water compartment Elevation differences within the water compartments were investigated through the digital elevation map. With proper geographical information systems operations statistical data about the variation of elevation for every water compartment was produced. This data included mean value, range and standard deviation. It was observed that in compartments with higher standard deviation more distinct values were observed. But in this case distinction was not systematic as it was in the previous parameter. (ie. Effect of seasons were always in a way that will cause a higher risk in Risk Model results, but variability of elevation might lead to higher or lower risk values) Main difference is, in WB21 method a single elevation (ie. Mean elevation) was used for the entire water compartment while in the risk model digital elevation model was used. This led to real elevation data in the scale of 25 m by 25 m pixels. This might have an increasing or decreasing effect on risk values. 67 Consider an event with a maximum groundwater level a little bit lower than the mean value of the entire water compartment. In this case WB21 method will not give any damage since the mean value is not exceeded and this is not considered as an event. But on the other hand Risk Model will calculate damage for pixels that lie below that groundwater level. This will lead the Risk Model to give higher results compared with the WB21 method. On the other hand when we consider an event with a groundwater level just above the mean elevation level, WB21 method will react as if the entire water compartment is flooded. But it is not the actual case. Areas above this groundwater level is not inundated, thus does not introduce any damage. Risk Method takes this fact into account and does not introduce any damage for the pixels that are above the groundwater level. Two examples mentioned above show that an approach based on DEM will be more accurate. 4.5.3. Land use It was also observed that the difference was greater in compartments where the percentage of agriculture and horticulture was higher. This difference is due to the fact that maximum damage coefficients for agriculture and horticulture are greater than grassland. Thus if the damage functions are different, difference in risk will be higher for agriculture compared with grass land. 68 4.6. Conclusions In this chapter, WB21 damage assessment method for single events were modeled in a way that 100 year period can be simulated and an annual average risk can be obtained as an outcome and a GIS based risk model was used to calculate the risk in the same area. Results were compared leading to following conclusions. 1- The risk model can be used for calculation of risk for floods due to precipitation exceeding drainage capacity with small modifications. Yet the risk value alone is not sufficient to judge on effectiveness of different methods unless they are modeled by exactly the same methodology since the results are affected largely by the way the damage is modeled. 2- There exist differences between two results. When the rationale behind this difference was further investigated, two main parameters were seen to be significantly effective. These are; - Occurrence season of events - Variation in elevation within a water compartment. 3- Time of occurrence must be taken into account for more accurate results, as the crop loss will be less in event occurring in winter compared with the events occurring in growth season. It was noted that this factor was not considered in the Risk Model used. 4- Variations in elevation within a polder are also effective on the resulting risk. If this variation is not included in the risk model, deviations from the real risk will occur in the results. This deviation is can be either in a way that will increase the risk or in a way that will decrease the risk. It is not possible to predict its effect before hand. Risk Model used overcomes this problem by including the real elevation data in terms of digital elevation map and provides more accurate results. 69 5. Conclusions & Recommendations Due to climate change extreme precipitation events follow an increasing trend. Combined with the land subsidence and sea level rise, this leads to an increase in the frequency of rainfall induces regional floods in low lands. Also as a result of on going urbanization land value increases. As a combination of all these reasons, risk of floods due to rainfall exceeding drainage capacity gains importance. This study was carried out for investigating the risk calculation for floods due to rainfall exceeding drainage capacity. The research was in three folds, namely as research on existing flood risk models in chapter two, investigation of correlation between flood depth and flood duration parameters in chapter three and a case study in order to calculate the risk of flooding due to rainfall exceeding drainage capacity. Conclusions and recommendations concerning this study are as follows. 70 5.1. Conclusions 1- A new model must be developed since non of the existing models are capable of calculating risk for floods caused by precipitation exceeding drainage capacity due to flowing reasons. - For this kind of floods failure is not limited to one section. Meaning, failure probability differs from frequent floods with small damages to low frequency floods with higher damage. - For this kind of floods failure is not limited to one section. Meaning, failure probability differs from frequent floods with small damages to low frequency floods with higher damage. - Probability is also dependent on the elevation of the pixel. As a result probability will be spatially distributed. Current models are not capable of calculating risk for spatially distributed probability functions. - Existing models do not cover effects of high ground water levels. 2- Correlation between flood depth and flood duration was proved. This proof has great importance for calculation of flood risk for floods due to precipitation exceeding drainage capacity. Based on this correlation flood duration parameter can be disregarded and flood depth can be used as an indicative parameter which will cover both coefficients. This will decrease the computational workload significantly and make the calculation of risk for this kind of floods possible. 71 3- Risk analysis tool described in chapter 4 can be used for calculation of risk due to floods exceeding drainage capacity with small alterations. Comparisons showed that occurrence season of the events is an important parameter in risk calculations and it was not covered in the risk analysis tool. In order to acquire accurate results, this parameter has to be included in calculations. This can be done by altering the program in a way that seasonal duration density functions of water elevations will be used. 4- The way of modeling the damage has a vast effect on the risk. Thus risk value alone will not be sufficient for comparison of effectiveness of different measures unless the exact same methodology is used for both calculations. 72 5.2. Recommendations The risk of floods due to precipitation exceeding drainage capacity increased considerably in last decades. And none of the currently used models are capable of calculating this risk thus more studies must be carried on for development of such a model and integration of this model to commercially available models. It was proved that flood depth and flood duration are strongly correlated. This correlation allows elimination of one of these parameters from flood damage calculations. This is an important issue for rainfall induced regional floods’ risk derivation since it is calculation demands high calculation load and this load can be decreased by using this assumption. Comparisons of the Risk Model showed that elevation must be an integral part of risk calculation for this kind of floods. Thus a GIS based model which includes digital elevation map is necessary. Comparisons also showed a shortcoming of the Risk Model. The risk model does not include the effects of seasons in agricultural damage calculation. Especially it must be considered that extreme events occur more frequently in winter season, when there are no crops on the fields. Thus the damage introduced in winter must be significantly lower than the ones occurring in the growth season of the crops. This can be included in the Risk Model by creating seasonal frequency distribution functions for water levels. This means that a different distribution function must be prepared for every season and maximum damage coefficients must be determined for different seasons. This will increase the accuracy of the calculated risk considerably. 73 Finally the depth – damage functions used in the model were rather simple damage functions, which were build considering main rationales behind flood damage like root zones or building heights. These depth–damage functions must be calibrated according to flood data and functions for other land use types must be derived. 74 6. References Bruijn, K.M. de, Heijer, F. Den, 2001, Flood Damage Modeling in The Netherlands: Preliminary Report Status Quo, Trend and Event Analysis, WL Delft Hydraulics, Delft, The Netherlands Bruijn K.M. de, 2005, Resilience and Flood Risk Management: A systems Approach Applied to Lowland Rivers, Delft University Press Burnham, M. W., Dotson, H. W., Overview of the Flood Damage Analysis Program (HEC-FDA), 1997 October 20-22,1997; Pacific Grove, California. US Army Corps of Engineers, Hydrologic Engineering Center p 137-153 Defra, Department for Environment Food and Rural Affairs, July 2003, Flood and Coastal Erosion Risk Management Research News, Issue 4 Defra, Department for Environment Food and Rural Affairs, August 2004, Modelling and Decision Support Framework (MDSF): History & Overview Defra, Department for Environment Food and Rural Affairs, May 2004, Modelling and Decision Support Framework (MDSF): Procedures Version 3.1 Dutta, D., Herath, S., Musiake, K., 2001, Direct Flood Damage Modeling Towards Urban Flood Risk Management, International Center for Urban Safety Engineering (ICUS/INCEDE), IIS, The University of Tokyo, Japan Penning-Rowsell, E.C., Chatterton, J.B., Day, H.J., Ford, D.T., Greenaway, M.A., Smith, D.I., Wood, T.R., Witts, R.C., 1987, Comparative Aspects of Computerized Floodplain Data Management, Journal of Water Resources Planning and Management, Vol.113, No.6 FEMA, Federal Emergency Management Agency, August 2004, Using HAZUS-MH for Risk Assessment: How-To Guide Hoes, Olivier, 2005, Risk Assessment to Quantify the Interaction Between Land Use and Water Management, ERSA-Congress, Amsterdam, The Netherlands IPCC, International Panel on Climate Change, 2001, Climate Change 2001: Impacts, Adaptation and Vulnerability, Cambridge University Press 75 Jonkman, S.N., Brinkhuis-Jak, M., Kok, M., 2004, Cost Benefit Analysis and Flood Damage Mitigation in the Netherlands, HERON, vol. 49, issue 1 Lekuthai, A., Vongvisessomjai, S., 2001, Intangible Flood Damage Quantification, Water Resources Management, Vol. 15, No. 05 pp:343-362 NR&M, Queensland Government Natural Resources and Mines Department, 2002, Guidance on the Assessment of Tangible Flood Damages Penning-Rowsell, E. et al., 2003, The Benefits of Flood and Coastal Defence: Techniques and Data for 2003, Flood Hazard Research Centre (FHRC), in press Penning-Rowsell, E. et al., 2005, Guidelines for Socio-Economic Flood Damage Evaluation: 1st Draft Version, FLOODsite Risk Frontiers, 2002, Risk Frontiers Quarterly Newsletter, vol. 1, no. 4, July 2002 USACE, 1988, National Economic Development Procedures Manual: United States Army Crops of Engineers, Fort Collins, USA USACE, 1998, HEC-FDA Flood Damage Reduction Analysis: User’s Manual, United States Army Crops of Engineers, USA 76 7. Appendix List of appendix: 1. 2. 3. 4. 5. Flood depth – Flood duration graphs for 12 must common soil types Frequency distribution graphs of water elevations for water compartments Script designed for WB21 model Output file of the WB21 script Statistical information on elevation data of water compartments 77 1 - Flood depth – Flood duration graphs for 12 must common soil types Sand Maximum - Average 0 0 100 200 300 400 500 600 -0.1 -0.2 Depth (m) -0.3 y = 0.0006x - 0.6856 2 R = 0.7237 k -0.4 Average Linear (Average) -0.5 -0.6 -0.7 -0.8 Duration (h) Sand Maximum - Maximum 0.6 y = 0.0022x - 0.6837 2 R = 0.7038 0.4 Depth (m) 0.2 0 0 100 200 300 400 500 600 -0.2 Maximum Linear (Maximum) -0.4 -0.6 -0.8 Duration (h) 78 Sand Average - Average 0 0 50 100 150 200 250 300 -0.1 -0.2 Average Linear (Average) Depth (m) -0.3 y = 0.0009x - 0.6829 2 R = 0.8016 -0.4 -0.5 -0.6 -0.7 -0.8 Duration (h) Sand Average - Maximum 0.6 y = 0.0041x - 0.6816 2 R = 0.7691 0.4 Depth (m) 0.2 0 0 50 100 150 200 250 300 -0.2 Maximum Linear (Maximum) -0.4 -0.6 -0.8 Duration (h) 79 Sand Minimum - Average 0 0 50 100 150 200 250 300 350 400 450 500 -0.1 -0.2 Depth (m) -0.3 y = 0.0006x - 0.6875 2 R = 0.7354 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Sand Minimum - Maximum 0.6 0.4 y = 0.0023x - 0.6886 2 R = 0.7178 Depth (m) 0.2 0 0 50 100 150 200 250 300 350 400 450 500 -0.2 Maximum Linear (Maximum) -0.4 -0.6 -0.8 Duration (h) 80 Peat Maximum - Average 0 0 50 100 150 200 250 300 350 -0.1 -0.2 Depth (m) -0.3 y = 0.001x - 0.6761 2 R = 0.7477 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Peat Maximum - Maximum 0.8 y = 0.0042x - 0.6568 2 R = 0.6922 0.6 0.4 Depth (m) 0.2 0 0 50 100 150 200 250 300 350 -0.2 Maximum Linear (Maximum) -0.4 -0.6 -0.8 Duration (h) 81 Peat Average - Average 0 0 50 100 150 200 250 300 350 y = 0.0017x - 0.6614 2 R = 0.623 -0.1 -0.2 Depth (m) -0.3 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Peat Average - Maximum 1.2 y = 0.0051x - 0.612 2 R = 0.5223 1 0.8 0.6 Depth (m) 0.4 Maximum Linear (Maximum) 0.2 0 0 50 100 150 200 250 300 350 -0.2 -0.4 -0.6 -0.8 Duration (h) 82 Peat Minimum - Average 0 0 50 100 150 200 250 300 350 -0.1 -0.2 y = 0.0012x - 0.6549 2 R = 0.3586 Depth (m) -0.3 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Peat Minimum - Maximum 1 y = 0.0047x - 0.615 2 R = 0.4254 0.8 0.6 Depth (m) 0.4 0.2 0 0 50 100 150 200 -0.2 250 300 350 Maximum Linear (Maximum) -0.4 -0.6 -0.8 Duration (h) 83 Clay Maximum - Average 0.1 0 0 50 100 150 200 250 y = 0.0018x - 0.6594 2 R = 0.5713 300 350 400 450 -0.1 Depth (m) -0.2 -0.3 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Clay Maximum - Maximum 2 1.5 y = 0.0053x - 0.6125 2 R = 0.4948 Depth (m) 1 g 0.5 Maximum Linear (Maximum) 0 0 50 100 150 200 250 300 350 400 450 -0.5 -1 Duration (h) 84 Clay Average - Average 0.1 0 0 50 100 150 200 250 y = 0.0017x - 0.6551 2 R = 0.4824 300 350 400 450 -0.1 Depth (m) -0.2 -0.3 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Clay Average - Maximum 2 y = 0.0054x - 0.5968 2 R = 0.4414 1.5 Depth (m) 1 Maximum Linear (Maximum) 0.5 0 0 50 100 150 200 250 300 350 400 450 -0.5 -1 Duration (h) 85 Clay Minimum - Average 0 0 50 100 150 200 250 300 350 400 -0.1 y = 0.0018x - 0.6523 2 R = 0.45 -0.2 Depth (m) -0.3 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Clay Minimum - Maximum 1.5 y = 0.0055x - 0.5938 2 R = 0.4309 1 Depth (m) 0.5 Maximum Linear (Maximum) 0 0 50 100 150 200 250 300 350 400 -0.5 -1 Duration (h) 86 Silt Maximum - Average 0 0 100 200 300 400 500 600 -0.1 y = 0.001x - 0.6817 2 R = 0.707 -0.2 Depth (m) -0.3 -0.4 -0.5 Average Linear (Average) -0.6 -0.7 -0.8 Duration (h) Silt Maximum - Maximum 1 y = 0.0031x - 0.6651 2 R = 0.686 0.8 0.6 0.4 Depth (m) Maximum Linear (Maximum) 0.2 0 0 100 200 300 400 500 600 -0.2 -0.4 -0.6 -0.8 Duration (h) 87 Silt Average - Average 0.4 y = 0.0021x - 0.6362 2 R = 0.3611 0.2 0 Depth (m) 0 50 100 150 200 250 300 350 400 450 -0.2 -0.4 Average Linear (Average) -0.6 -0.8 Duration (h) Silt Average - Maximum 2.5 y = 0.0062x - 0.5751 2 R = 0.3767 2 Depth (m) 1.5 1 Maximum Linear (Maximum) 0.5 0 0 50 100 150 200 250 300 350 400 450 -0.5 -1 Duration (h) 88 Silt Minimum - Average 0 0 100 200 300 400 500 600 -0.1 -0.2 Average Linear (Average) Depth (m) -0.3 y = 0.0006x - 0.6863 2 R = 0.7241 -0.4 -0.5 -0.6 -0.7 -0.8 Duration (h) Silt Minimum - Maximum 0.6 y = 0.0021x - 0.6862 2 R = 0.7057 0.4 Depth (m) 0.2 0 0 100 200 300 400 500 600 -0.2 Maximum Linear (Maximum) -0.4 -0.6 -0.8 Duration (h) 2 - Frequency distribution graphs of water elevations for water compartments 89 Gumbel Distribution Location: 306 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -6 0.1 0.2 - - - - - -0.5 - - - - - - - 0.8 - - - - 0.9 - - 0.95 - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.08 X0 = -6.13 Gumbel Distribution Location: 312 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -6 0.1 0.2 - - - - 0.5 - - - - - - - 0.8 - - - 0.9- - -0.95 - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.09 X0 = -6.16 Gumbel Distribution Location: 317 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -6 0.1 0.2 - -0.5 - - - - - - - 0.8 - - - -0.9 - - -0.95 - - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.08 X0 = -6.17 90 Gumbel Distribution Location: 322 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -6 0.1 0.2 - - - - - -0.5 - - - - - - -0.8 - - - - 0.9 - - 0.95 - - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.09 X0 = -6.07 Gumbel Distribution Location: 325 Return Period 1.111 2 5 10 20 100 1,000 10,000 -5.3 -5.4 -5.45 -5.5 -5.55 -5.6 -5.65 -5.7 -5.75 -5.8 -5.85 -5.9 -5.95 -6 -6.05 -6.1 -6.15 -6.2 0.1 0.2 - - - - 0.5 - - - - - - - 0.8 - - - - - 0.9 - - 0.95 - - - 0.99 - - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.07 X0 = -6.12 Gumbel Distribution Location: 330 Return Period 1.111 2 5 10 20 100 1,000 10,000 -5.4 reduced variate observed frequencies reduced variate observed frequencies -5.35 -5.45 -5.5 -5.55 -5.6 -5.65 -5.7 -5.75 -5.8 -5.85 -5.9 -5.95 -6 0.1 -0.2 - - - - - -0.5 -- --- - 0.8 - - - - 0.9 --- 0.95 - - - -0.99 - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.05 X0 = -5.94 91 Gumbel Distribution Location: 336 Return Period 1.111 2 5 10 20 100 1,000 10,000 reduced variate observed frequencies -5.5 -5.55 -5.6 -5.65 -5.7 -5.75 -5.8 -5.85 -5.9 -5.95 -6 0.1 - 0.2 - - - - - -0.5 - - - - - - -0.8 - - - 0.9- - - 0.95 - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.94 Gumbel Distribution Location: 337 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5 -6 0.1 0.2 0.5 0.8 - - - - -0.9 - - - -0.95 - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.10 X0 = -6.01 Gumbel Distribution Location: 344 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5 -6 0.1 0.2 0.5 0.8 - - - - - 0.9 - - 0.95 - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.10 X0 = -6.00 92 Gumbel Distribution Location: 346 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5.58 -5.6 -5.62 -5.64 -5.66 -5.68 -5.7 -5.72 -5.74 -5.76 -5.78 -5.8 -5.82 -5.84 -5.86 -5.88 -5.9 -5.92 -5.94 -5.96 -5.98 -6 0.1 - 0.2 - - - - -0.5 - -- - - - -0.8 - 0.9 - - - -0.95 - - - 0.99 - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.03 X0 = -5.92 Gumbel Distribution Location: 352 Return Period 1.111 2 5 10 20 100 1,000 10,000 -2.84 -2.88 -2.9 -2.92 -2.94 -2.96 -2.98 -3 -3.02 -3.04 -3.06 -3.08 -3.1 -3.12 -3.14 -3.16 -3.18 -3.2 -3.22 0.1 - 0.2 - - - - - -0.5 - - - - - - -0.8 - - 0.9- - 0.95 - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.03 X0 = -3.14 Gumbel Distribution Location: 359 Return Period 1.111 2 5 10 20 100 1,000 10,000 -2.94 reduced variate observed frequencies reduced variate observed frequencies -2.86 -2.96 -2.98 -3 -3.02 -3.04 -3.06 -3.08 -3.1 -3.12 -3.14 -3.16 -3.18 -3.2 -3.22 -3.24 0.1 0.2- - - - - 0.5 - - - - - - - 0.8 - - - 0.9 - - - - 0.95 - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.02 X0 = -3.20 93 Gumbel Distribution Location: 364 Return Period 1.111 2 5 10 20 100 1,000 10,000 -2.84 -2.88 -2.9 -2.92 -2.94 -2.96 -2.98 -3 -3.02 -3.04 -3.06 -3.08 -3.1 -3.12 -3.14 -3.16 -3.18 -3.2 -3.22 0.1- 0.2 - - - - - - 0.5 - - - - - - - - -0.8 - - - 0.9 - - 0.95- - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.03 X0 = -3.14 Gumbel Distribution Location: 367 Return Period 1.111 2 5 10 20 100 1,000 10,000 -5.55 -5.6 -5.65 -5.7 -5.75 -5.8 -5.85 -5.9 -5.95 -6 0.1 0.2 - - - - - -0.5 - - - - - - - 0.8 - - - - 0.9 - - 0.95 - - - - 0.99 - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.95 Gumbel Distribution Location: 373 Return Period 1.111 2 5 10 20 100 1,000 10,000 -5.5 reduced variate observed frequencies reduced variate observed frequencies reduced variate observed frequencies -2.86 -5.55 -5.6 -5.65 -5.7 -5.75 -5.8 -5.85 -5.9 -5.95 -6 0.1 0.2 - - - - - - 0.5 - - - - - - - 0.8 - - - - 0.9 - - 0.95 - - - - 0.99 - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.96 94 Gumbel Distribution Location: 377 Return Period 1.111 2 5 10 20 100 1,000 10,000 reduced variate observed frequencies -5.45 -5.5 -5.55 -5.6 -5.65 -5.7 -5.75 -5.8 -5.85 -5.9 -5.95 -6 -6.05 0.1 0.2- - - - -0.5 - - - - - - - 0.8 - - - -0.9 - -0.95 - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.05 X0 = -5.99 Gumbel Distribution Location: 383 Return Period 1.111 2 5 10 20 100 1,000 10,000 -4.9 -4.95 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 0.1 - 0.2 - - - - - 0.5 - - - - - - - -0.8 - - - 0.9 - - - -0.95 - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.28 Gumbel Distribution Location: 385 Return Period 1.111 2 5 10 20 100 1,000 10,000 -4.85 reduced variate observed frequencies reduced variate observed frequencies -4.85 -4.9 -4.95 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 0.1 -0.2 - - - - - 0.5 - - - - - - - 0.8 -- - 0.9 -- - -0.95 - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.28 95 Gumbel Distribution Location: 389 Return Period 1.111 2 5 10 20 100 1,000 10,000 reduced variate observed frequencies -4.85 -4.9 -4.95 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 0.1 -0.2 - - - - - 0.5 - - - - - - - 0.8 -- - 0.9 - - - -0.95 - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.28 Gumbel Distribution Location: 395 Return Period 1.111 2 5 10 20 - 0.9 - - - -0.95 100 1,000 10,000 -4.9 -4.95 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 0.1 - 0.2 - - - - - 0.5 - - - - - - - 0.8 - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.28 Gumbel Distribution Location: 399 Return Period 1.111 reduced variate observed frequencies reduced variate observed frequencies -4.85 2 5 10 20 100 1,000 10,000 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 -5.4 -5.45 0.1 - 0.2 - - - - - 0.5 - - - - - - - -0.8 - - - 0.9 - - - -0.95 -- - 0.99- - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.36 96 Gumbel Distribution Location: 402 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 -5.4 -5.45 0.1 - 0.2 - - - - - -0.5 - - - - - - - 0.8 - - - 0.9 -- - -0.95 - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.35 Gumbel Distribution Location: 407 Return Period 1.111 2 5 10 20 100 1,000 10,000 reduced variate observed frequencies -2.55 -2.6 -2.65 -2.7 -2.75 -2.8 -2.85 -2.9 -2.95 -3 -3.05 -3.1 -3.15 0.1- -0.2 - - - - - 0.5 - - - - - - - -0.8- - - -0.9- 0.95 - --- - 0.99 - - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.05 X0 = -3.04 Gumbel Distribution Location: 411 Return Period 1.111 2 5 10 20 -0.9- 0.95 - - 100 1,000 10,000 reduced variate observed frequencies -2.4 -2.45 -2.5 -2.55 -2.6 -2.65 -2.7 -2.75 -2.8 -2.85 -2.9 -2.95 0.1 - 0.2 - - - - - -0.5 - - - - - - - 0.8 - - - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -2.83 97 Gumbel Distribution Location: 414 Return Period 1.111 2 5 10 20 100 1,000 10,000 reduced variate observed frequencies -4.8 -4.85 -4.9 -4.95 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 0.1 -0.2 - - - - - 0.5 - - - - - - - 0.8 -- - - 0.9 - - -0.95 - - 0.99 - - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.04 X0 = -5.27 Gumbel Distribution Location: 419 Return Period 1.111 2 5 10 20 100 1,000 10,000 reduced variate observed frequencies -3.09 -3.1 -3.11 -3.12 -3.13 -3.14 -3.15 -3.16 -3.17 -3.18 -3.19 0.1 - - 0.2 - - - - - -0.5 - - - - - - - 0.8 - -- -0.9 - - 0.95- - - 0.99 - - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.01 X0 = -3.17 Gumbel Distribution Location: 423 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5 -6 0.1 0.2 0.5 - - - 0.8 - - - - - 0.9 - - - 0.95 - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.11 X0 = -5.95 98 Gumbel Distribution Location: 427 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5 -6 0.1 0.2 0.5 - - -0.8 - -- - 0.9 - - - - 0.95 - - -0.99 - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.12 X0 = -5.97 Gumbel Distribution Location: 430 Return Period reduced variate observed frequencies 1.111 2 5 10 20 100 1,000 10,000 -5 -6 0.1 0.2 0.5 - - - 0.8 - - - - -0.9- - 0.95 - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.11 X0 = -5.93 Gumbel Distribution Location: 434 Return Period 1.111 2 5 10 20 100 1,000 10,000 -4.45 reduced variate observed frequencies -4.5 -4.55 -4.6 -4.65 -4.7 -4.75 -4.8 -4.85 -4.9 -4.95 -5 -5.05 -5.1 -5.15 -5.2 -5.25 -5.3 -5.35 -5.4 0.1 -0.2 - - - - - 0.5 - - - - - - -0.8 - - - 0.9 - -0.95 - - - - 0.99 - - - 0.999 - - - - -1 Frequencies regression line upper confidence limit data reduced variate observed frequencies Gumbel Distribution low er confidence limit data B = 0.07 X0 = -5.25 99 3 -Script designed for WB21 model Option Compare Database Option Base 1 Sub wb21() Dim time1 c1bouwspring = Array(8 * 10 ^ -5, 9 * 10 ^ -5, 8 * 10 ^ -5, 9 * 10 ^ -5, 10 * 10 ^ -5) c1bouwsummer = Array(14 * 10 ^ -5, 15 * 10 ^ -5, 14 * 10 ^ -5, 16 * 10 ^ -5, 16 * 10 ^ -5) c1bouwautumn = Array(7 * 10 ^ -5, 7 * 10 ^ -5, 7 * 10 ^ -5, 8 * 10 ^ -5, 8 * 10 ^ -5) c1bouwwinter = Array(0, 0, 0, 0, 0) c0spring = Array(20 * 10 ^ -5, 10 * 10 ^ -5, 5 * 10 ^ -5, 10 * 10 ^ -5, 0) c0summer = Array(26 * 10 ^ -5, 17 * 10 ^ -5, 17 * 10 ^ -5, 17 * 10 ^ -5, 0) c0autumn = Array(6 * 10 ^ -5, 6 * 10 ^ -5, 8 * 10 ^ -5, 6 * 10 ^ -5, 0) c0winter = Array(0, 0, 0, 0, 0) c1hoogspring = Array(14 * 10 ^ -5, 14 * 10 ^ -5, 14 * 10 ^ -5, 16 * 10 ^ -5, 16 * 10 ^ -5) c1hoogsummer = Array(24 * 10 ^ -5, 24 * 10 ^ -5, 23 * 10 ^ -5, 27 * 10 ^ -5, 27 * 10 ^ -5) c1hoogautumn = Array(11 * 10 ^ -5, 12 * 10 ^ -5, 11 * 10 ^ -5, 13 * 10 ^ -5, 13 * 10 ^ -5) c1hoogwinter = Array(0, 0, 0, 0, 0) c2rest = Array(21 * 10 ^ -5, 21 * 10 ^ -5, 21 * 10 ^ -5, 7 * 10 ^ -5, 5 * 10 ^ -5) c2winter = Array(0, 0, 0, 0, 0) Maximumdamage = Array(900, 3600, 18000) Dim wc(40) As Variant Dim compdamage(40) As Variant nodenumber2 = 0 time1 = 0 hmax = -100 level1 = -100 hsum = 0 dursum = 0 eventsum = 0 location = 0 duration = 0 eventsum = 0 eventspring = 0 eventsummer = 0 eventautumn = 0 eventwinter = 0 durspring = 0 dursummer = 0 durautumn = 0 durwinter = 0 skowcount = 0 sowcount = 0 durationexceedcount = 0 damagefuncskow = 0 damagefuncsow = 0 damagefuncduration = 0 yearlydamageagg = 0 yearlydamagegrass = 0 nodecount = 1 Open "d:\berkeldin.txt" For Binary As #1 Open "d:\berkeldout.txt" For Output As #2 Open "d:\berkeldstat.txt" For Output As #3 Do While location < LOF(1) Input #1, nodenumber1, month1, level location = Loc(1) time1 = time1 + 1 year1 = time1 / 365 100 If nodenumber1 <> nodenumber2 Then If nodenumber2 <> 0 Then Print #2, "-----------------------------------------------------------------" Print #2, Print #2, "*Location:"; nodenumber2 Print #2, "*Water compartment:"; watercomp Print #2, Print #2, "*Number of events:"; eventsum Print #2, Print #2, "*Number of events in spring:"; eventspring Print #2, "*Number of events in summer:"; eventsummer Print #2, "*Number of events in autumn:"; eventautumn Print #2, "*Number of events in winter:"; eventwinter Print #2, Print #2, "*Duration of events in spring:"; durspring Print #2, "*Duration of events in summer:"; dursummer Print #2, "*Duration of events in autumn:"; durautumn Print #2, "*Duration of events in winter:"; durwinter Print #2, Print #2, "*Number of events calculated by skow:"; skowcount Print #2, "*Number of events calculated by sow:"; sowcount Print #2, "*Number of events exceeding 3 days:"; durationexceedcount Print #2, Print #2, "*Damage function sum calculated by skow:"; damagefuncskow Print #2, "*Damage function sum calculated by sow:"; damagefuncsow Print #2, "*Damage function sum calculated due to duration exceeding 3 days:"; damagefuncduration Print #2, Print #2, "*Total duration above target level:"; dursum Print #2, "*Total simulation period in days:"; time1 Print #2, "*Total simulation period in years:"; year1 Print #2, Print #2, "*Total damage function for grass:"; damagefuncsumgrass Print #2, "*Total damage function for aggriculture:"; damagefuncsumagg Print #2, Print #2, "*Total damage for grass:"; totaldamagegrass Print #2, "*Total damage for aggriculture;"; totaldamageagg Print #2, "*Total damage:"; totaldamage Print #2, "*Anual avarage risk:"; anualaverage Print #2, Print #2, "-----------------------------------------------------------------" Print #3, "-----------------------------------------------------------------" Print #3, Print #3, "*Location:"; nodenumber2 Print #3, "*Water compartment:"; watercomp Print #3, Print #3, "*Number of events:"; eventsum Print #3, Print #3, "*Number of events in spring:"; eventspring Print #3, "*Number of events in summer:"; eventsummer Print #3, "*Number of events in autumn:"; eventautumn Print #3, "*Number of events in winter:"; eventwinter Print #3, Print #3, "*Duration of events in spring:"; durspring Print #3, "*Duration of events in summer:"; dursummer Print #3, "*Duration of events in autumn:"; durautumn Print #3, "*Duration of events in winter:"; durwinter Print #3, Print #3, "*Number of events calculated by skow:"; skowcount Print #3, "*Number of events calculated by sow:"; sowcount Print #3, "*Number of events exceeding 3 days:"; durationexceedcount Print #3, Print #3, "*Damage function sum calculated by skow:"; damagefuncskow Print #3, "*Damage function sum calculated by sow:"; damagefuncsow Print #3, "*Damage function sum calculated due to duration exceeding 3 days:"; damagefuncduration Print #3, Print #3, "*Total duration above target level:"; dursum Print #3, "*Total simulation period in days:"; time1 101 Print #3, "*Total simulation period in years:"; year1 Print #3, Print #3, "*Total damage function for grass:"; damagefuncsumgrass Print #3, "*Total damage function for aggriculture:"; damagefuncsumagg Print #3, Print #3, "*Total damage for grass:"; totaldamagegrass Print #3, "*Total damage for aggriculture;"; totaldamageagg Print #3, "*Total damage:"; totaldamage Print #3, "*Anual avarage risk:"; anualaverage Print #3, Print #3, "-----------------------------------------------------------------" wc(nodecount) = watercomp compdamage(nodecount) = anualaverage nodecount = nodecount + 1 End If Print #2, "*Duration", "Height", "Mode", "Damage Coefficient Aggriculture", "Damage Coefficient Grass" nodenumber2 = nodenumber1 eventsum = 0 eventspring = 0 eventsummer = 0 eventautumn = 0 eventwinter = 0 durspring = 0 dursummer = 0 durautumn = 0 durwinter = 0 skowcount = 0 sowcount = 0 durationexceedcount = 0 damagefuncskow = 0 damagefuncsow = 0 damagefuncduration = 0 dursum = 0 time1 = 1 damagefuncsumgrass = 0 damagefuncsumagg = 0 totaldamage = 0 'coef = Array(%grass, soiltype, targetlevel, area, %aggriculture, watercompartment) 'soil type 1=zand or leermarm 2=lichte zavel/lemig 3=zware zawel/moerige 4=lichte klei 5=zware klei If nodenumber1 = 288 Then coef = Array(0.289, 4, -5.3, 135.75, 0.248, 306) If nodenumber1 = 292 Then coef = Array(0.682, 4, -5.29, 78.56, 0.086, 344) If nodenumber1 = 309 Then coef = Array(0.275, 4, -5.32, 100.56, 0.144, 312) If nodenumber1 = 315 Then coef = Array(0.646, 4, -5.27, 82.63, 0.161, 317) If nodenumber1 = 321 Then coef = Array(0.558, 4, -5.48, 78.38, 0.436, 322) If nodenumber1 = 323 Then coef = Array(0.172, 4, -3.84, 95, 0, 325) If nodenumber1 = 328 Then coef = Array(0.263, 2, -5.19, 55.69, 0, 330) If nodenumber1 = 333 Then coef = Array(0.252, 4, -5.14, 30.75, 0, 336) If nodenumber1 = 338 Then coef = Array(0.575, 4, -4.88, 49.25, 0.056, 337) If nodenumber1 = 348 Then coef = Array(0.678, 4, -4.69, 120.25, 0.012, 346) If nodenumber1 = 354 Then coef = Array(0.513, 4, -2.68, 55.56, 0.141, 352) If nodenumber1 = 358 Then coef = Array(0.277, 4, -2.65, 27.56, 0, 359) If nodenumber1 = 362 Then coef = Array(0.474, 4, -2.93, 22.81, 0, 364) If nodenumber1 = 369 Then coef = Array(0.291, 4, -2.56, 24.5, 0, 367) If nodenumber1 = 370 Then coef = Array(0.459, 4, -5.3, 80.19, 0.084, 373) If nodenumber1 = 375 Then coef = Array(0.636, 4, -5.27, 66.75, 0.155, 377) If nodenumber1 = 381 Then coef = Array(0.495, 4, -4.84, 40.94, 0.011, 383) If nodenumber1 = 386 Then coef = Array(0.891, 4, -5.18, 50, 0, 385) If nodenumber1 = 392 Then coef = Array(0.565, 2, -5.01, 51.06, 0.174, 389) If nodenumber1 = 393 Then coef = Array(0.864, 4, -5.02, 33.06, 0, 395) If nodenumber1 = 397 Then coef = Array(0.609, 2, -4.97, 84.63, 0.077, 399) If nodenumber1 = 403 Then coef = Array(0.745, 4, -4.64, 67.69, 0.01, 402) If nodenumber1 = 406 Then coef = Array(0.555, 4, -2.87, 94.81, 0.042, 407) If nodenumber1 = 409 Then coef = Array(0.47, 4, -2.77, 116.56, 0.064, 411) If nodenumber1 = 415 Then coef = Array(0.902, 2, -5.03, 35.25, 0, 414) 102 If nodenumber1 = 418 Then coef = Array(0.701, 2, -2.98, 41.19, 0, 419) If nodenumber1 = 424 Then coef = Array(0.699, 2, -5.32, 57.5, 0.061, 423) If nodenumber1 = 425 Then coef = Array(0.783, 2, -5.22, 81.75, 0.038, 427) If nodenumber1 = 431 Then coef = Array(0.945, 2, -5.39, 94.38, 0.054, 430) If nodenumber1 = 432 Then coef = Array(0.873, 2, -5.12, 99.56, 0, 434) If nodenumber1 = 467 Then coef = Array(0, 2, -9, 0, 0, 470) watercomp = coef(6) End If If level > coef(3) Then height1 = level - coef(3) duration = duration + 1 hsum = hsum + height1 level1 = level If hmax < height1 Then hmax = height1 End If If level < coef(3) And level1 > coef(3) Then havgr = hsum / duration sow = hmax * duration * 100 skow = hmax * hmax * duration * 10000 If month1 > 2 And month1 < 6 Then durspring = durspring + duration eventspring = eventspring + 1 c0 = c0spring(coef(2)) c1b = c1bouwspring(coef(2)) c1h = c1hoogspring(coef(2)) c2 = c2rest(coef(2)) End If If month1 > 5 And month1 < 9 Then dursummer = dursummer + duration eventsummer = eventsummer + 1 c0 = c0summer(coef(2)) c1b = c1bouwsummer(coef(2)) c1h = c1hoogsummer(coef(2)) c2 = c2rest(coef(2)) End If If month1 > 8 And month1 < 11 Then durautumn = durautumn + duration eventautumn = eventautumn + 1 c0 = c0autumn(coef(2)) c1b = c1bouwautumn(coef(2)) c1h = c1hoogautumn(coef(2)) c2 = c2rest(coef(2)) End If If month1 > 10 Or month1 < 3 Then durwinter = durwinter + duration eventwinter = eventwinter + 1 c0 = c0winter(coef(2)) c1b = c1bouwwinter(coef(2)) c1h = c1hoogwinter(coef(2)) c2 = c2winter(coef(2)) End If 'grass damage damagefuncgrass = c0 * sow yearlydamagegrass = yearlydamagegrass + damagefuncgrass If yearlydamagegrass > 1 Then yearlydamagegrass = 1 'aggricultural damage 103 d1 = c1b * sow d2 = c2 * skow If d1 > d2 Then damagefuncagg = d1 Else damagefuncagg = d2 If damagefuncagg = c2 * skow Then skowcount = skowcount + 1 If damagefuncagg > 1 Then damagefuncagg = 1 damagefuncskow = damagefuncskow + damagefuncagg Mode = "skow" End If If duration >= 4 Then durationexceedcount = durationexceedcount + 1 End If If damagefuncagg <> c2 * skow And damagefuncagg <> 1 Then sowcount = sowcount + 1 If damagefuncagg > 1 Then damagefuncagg = 1 damagefuncsow = damagefuncsow + damagefuncagg Mode = "sow" End If yearlydamageagg = yearlydamageagg + damagefuncagg If yearlydamageagg > 1 Then yearlydamageagg = 1 Print #2, duration; Tab; hmax; Tab; Mode; Tab; damagefuncagg; Tab; damagefuncgrass eventsum = eventsum + 1 dursum = dursum + duration duration = 0 hsum = 0 hmax = -100 level1 = -100 damagefuncgrass = 0 damagefuncagg = 0 End If If month1 = 1 Then damagefuncsumgrass = damagefuncsumgrass + yearlydamagegrass yearlydamagegrass = 0 damagefuncsumagg = damagefuncsumagg + yearlydamageagg yearlydamageagg = 0 End If totaldamagegrass = damagefuncsumgrass * coef(1) * coef(4) * 900 totaldamageagg = damagefuncsumagg * coef(5) * coef(4) * 3600 totaldamage = (damagefuncsumgrass * coef(1) * coef(4) * 900) + (damagefuncsumagg * coef(5) * coef(4) * 3600) anualaverage = totaldamage / year1 Loop 'final summary print Print #3, Print #3, "Water Compartment"; Tab; "Anual Damage" i=1 Do While i <= 38 Print #3, wc(i); Tab; compdamage(i) i=i+1 Loop Close #1 Close #2 Close #3 104 ----------------------------------------------------------------*Location: 288 *Water compartment: 306 *Number of events: 7 *Number of events in spring: 1 *Number of events in summer: 1 *Number of events in autumn: 2 *Number of events in winter: 3 *Duration of events in spring: 1 *Duration of events in summer: 1 *Duration of events in autumn: 3 *Duration of events in winter: 5 *Number of events calculated by skow: 7 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0.1666 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 10 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.0092 *Total damage function for aggriculture: 0.1666 *Total damage for grass: 324.83889 *Total damage for aggriculture; 20191.52016 *Total damage: 20516.35905 *Anual avarage risk: 205.017550600942 --------------------------------------------------------------------------------------------------------------------------------*Location: 292 *Water compartment: 344 *Number of events: 592 *Number of events in spring: 58 *Number of events in summer: 68 *Number of events in autumn: 114 *Number of events in winter: 352 *Duration of events in spring: 109 *Duration of events in summer: 128 *Duration of events in autumn: 280 *Duration of events in winter: 895 *Number of events calculated by skow: 577 *Number of events calculated by sow: 15 *Number of events exceeding 3 days: 113 *Damage function sum calculated by skow: 23.2173 *Damage function sum calculated by sow: 0.00164 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 1412 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 1.1537 *Total damage function for aggriculture: 23.1328 *Total damage for grass: 55631.5616736 *Total damage for aggriculture; 562640.0329728 *Total damage: 618271.5946464 *Anual avarage risk: 6178.31495498921 ----------------------------------------------------------------- 105 ----------------------------------------------------------------*Location: 309 *Water compartment: 312 *Number of events: 2 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 1 *Number of events in winter: 1 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 2 *Duration of events in winter: 1 *Number of events calculated by skow: 2 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0.0617 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 3 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.0025 *Total damage function for aggriculture: 0.0617 *Total damage for grass: 62.2215 *Total damage for aggriculture; 3216.4397568 *Total damage: 3278.6612568 *Anual avarage risk: 32.7632743451788 --------------------------------------------------------------------------------------------------------------------------------*Location: 315 *Water compartment: 317 *Number of events: 0 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 0 *Number of events calculated by skow: 0 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 0 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 ----------------------------------------------------------------- 106 ----------------------------------------------------------------*Location: 321 *Water compartment: 322 *Number of events: 1 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 1 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 1 *Duration of events in winter: 0 *Number of events calculated by skow: 1 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0.00567 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 1 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.00054 *Total damage function for aggriculture: 0.00567 *Total damage for grass: 21.25571544 *Total damage for aggriculture; 697.55315616 *Total damage: 718.8088716 *Anual avarage risk: 7.18297207835515 --------------------------------------------------------------------------------------------------------------------------------*Location: 323 *Water compartment: 325 *Number of events: 0 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 0 *Number of events calculated by skow: 0 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 0 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 ----------------------------------------------------------------- 107 ----------------------------------------------------------------*Location: 328 *Water compartment: 330 *Number of events: 0 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 0 *Number of events calculated by skow: 0 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 0 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 --------------------------------------------------------------------------------------------------------------------------------*Location: 333 *Water compartment: 336 *Number of events: 2 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 2 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 3 *Number of events calculated by skow: 2 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 3 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 ----------------------------------------------------------------- 108 ----------------------------------------------------------------*Location: 338 *Water compartment: 337 *Number of events: 0 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 0 *Number of events calculated by skow: 0 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 0 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 --------------------------------------------------------------------------------------------------------------------------------*Location: 348 *Water compartment: 346 *Number of events: 0 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 0 *Number of events calculated by skow: 0 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 0 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 ----------------------------------------------------------------- 109 ----------------------------------------------------------------*Location: 354 *Water compartment: 352 *Number of events: 50 *Number of events in spring: 3 *Number of events in summer: 7 *Number of events in autumn: 15 *Number of events in winter: 25 *Duration of events in spring: 7 *Duration of events in summer: 12 *Duration of events in autumn: 23 *Duration of events in winter: 51 *Number of events calculated by skow: 49 *Number of events calculated by sow: 1 *Number of events exceeding 3 days: 2 *Damage function sum calculated by skow: 2.0291 *Damage function sum calculated by sow: 0.00032 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 93 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.0868 *Total damage function for aggriculture: 2.0293 *Total damage for grass: 2226.5981136 *Total damage for aggriculture; 57230.8381008 *Total damage: 59457.4362144 *Anual avarage risk: 594.151131201226 --------------------------------------------------------------------------------------------------------------------------------*Location: 358 *Water compartment: 359 *Number of events: 76 *Number of events in spring: 7 *Number of events in summer: 10 *Number of events in autumn: 24 *Number of events in winter: 35 *Duration of events in spring: 12 *Duration of events in summer: 17 *Duration of events in autumn: 37 *Duration of events in winter: 62 *Number of events calculated by skow: 73 *Number of events calculated by sow: 3 *Number of events exceeding 3 days: 2 *Damage function sum calculated by skow: 1.8824 *Damage function sum calculated by sow: 0.00057 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 128 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.1159 *Total damage function for aggriculture: 1.883 *Total damage for grass: 796.3150572 *Total damage for aggriculture; 0 *Total damage: 796.3150572 *Anual avarage risk: 7.95748222849477 ----------------------------------------------------------------- 110 ----------------------------------------------------------------*Location: 362 *Water compartment: 364 *Number of events: 669 *Number of events in spring: 136 *Number of events in summer: 58 *Number of events in autumn: 96 *Number of events in winter: 379 *Duration of events in spring: 1071 *Duration of events in summer: 285 *Duration of events in autumn: 783 *Duration of events in winter: 5088 *Number of events calculated by skow: 640 *Number of events calculated by sow: 29 *Number of events exceeding 3 days: 460 *Damage function sum calculated by skow: 83.874 *Damage function sum calculated by sow: 0.00464 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 7227 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 7.1127 *Total damage function for aggriculture: 57.5455 *Total damage for grass: 69211.8770742 *Total damage for aggriculture; 0 *Total damage: 69211.8770742 *Anual avarage risk: 691.626105570908 --------------------------------------------------------------------------------------------------------------------------------*Location: 369 *Water compartment: 367 *Number of events: 0 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 0 *Number of events calculated by skow: 0 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 0 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 ----------------------------------------------------------------- 111 ----------------------------------------------------------------*Location: 370 *Water compartment: 373 *Number of events: 66 *Number of events in spring: 6 *Number of events in summer: 9 *Number of events in autumn: 21 *Number of events in winter: 30 *Duration of events in spring: 11 *Duration of events in summer: 16 *Duration of events in autumn: 33 *Duration of events in winter: 78 *Number of events calculated by skow: 62 *Number of events calculated by sow: 4 *Number of events exceeding 3 days: 4 *Damage function sum calculated by skow: 0.2832 *Damage function sum calculated by sow: 0.00041 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 138 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.0472 *Total damage function for aggriculture: 0.2837 *Total damage for grass: 1563.5702808 *Total damage for aggriculture; 6879.5706672 *Total damage: 8443.140948 *Anual avarage risk: 84.3713093692164 --------------------------------------------------------------------------------------------------------------------------------*Location: 375 *Water compartment: 377 *Number of events: 73 *Number of events in spring: 4 *Number of events in summer: 4 *Number of events in autumn: 17 *Number of events in winter: 48 *Duration of events in spring: 9 *Duration of events in summer: 8 *Duration of events in autumn: 33 *Duration of events in winter: 104 *Number of events calculated by skow: 71 *Number of events calculated by sow: 2 *Number of events exceeding 3 days: 11 *Damage function sum calculated by skow: 2.5919 *Damage function sum calculated by sow: 0.0004 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 154 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.0836 *Total damage function for aggriculture: 2.5922 *Total damage for grass: 3194.16372 *Total damage for aggriculture; 96550.3773 *Total damage: 99744.54102 *Anual avarage risk: 996.735406896457 ----------------------------------------------------------------- 112 ----------------------------------------------------------------*Location: 381 *Water compartment: 383 *Number of events: 67 *Number of events in spring: 5 *Number of events in summer: 8 *Number of events in autumn: 20 *Number of events in winter: 34 *Duration of events in spring: 10 *Duration of events in summer: 14 *Duration of events in autumn: 33 *Duration of events in winter: 72 *Number of events calculated by skow: 64 *Number of events calculated by sow: 3 *Number of events exceeding 3 days: 5 *Damage function sum calculated by skow: 3.5183 *Damage function sum calculated by sow: 0.00032 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 129 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.1396 *Total damage function for aggriculture: 3.4285 *Total damage for grass: 2546.132292 *Total damage for aggriculture; 5558.366484 *Total damage: 8104.498776 *Anual avarage risk: 80.9872981777364 --------------------------------------------------------------------------------------------------------------------------------*Location: 386 *Water compartment: 385 *Number of events: 623 *Number of events in spring: 157 *Number of events in summer: 65 *Number of events in autumn: 87 *Number of events in winter: 314 *Duration of events in spring: 2320 *Duration of events in summer: 427 *Duration of events in autumn: 1010 *Duration of events in winter: 6578 *Number of events calculated by skow: 597 *Number of events calculated by sow: 26 *Number of events exceeding 3 days: 467 *Damage function sum calculated by skow: 118.5809 *Damage function sum calculated by sow: 0.00448 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 10335 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 14.4597 *Total damage function for aggriculture: 68.9031 *Total damage for grass: 579761.6715 *Total damage for aggriculture; 0 *Total damage: 579761.6715 *Anual avarage risk: 5793.489845521 ----------------------------------------------------------------- 113 ----------------------------------------------------------------*Location: 392 *Water compartment: 389 *Number of events: 25 *Number of events in spring: 2 *Number of events in summer: 2 *Number of events in autumn: 5 *Number of events in winter: 16 *Duration of events in spring: 7 *Duration of events in summer: 5 *Duration of events in autumn: 12 *Duration of events in winter: 59 *Number of events calculated by skow: 25 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 6 *Damage function sum calculated by skow: 0.7509 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 83 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.02 *Total damage function for aggriculture: 0.751 *Total damage for grass: 519.2802 *Total damage for aggriculture; 24019.971984 *Total damage: 24539.252184 *Anual avarage risk: 245.217846114001 --------------------------------------------------------------------------------------------------------------------------------*Location: 393 *Water compartment: 395 *Number of events: 266 *Number of events in spring: 17 *Number of events in summer: 17 *Number of events in autumn: 52 *Number of events in winter: 180 *Duration of events in spring: 42 *Duration of events in summer: 35 *Duration of events in autumn: 151 *Duration of events in winter: 451 *Number of events calculated by skow: 262 *Number of events calculated by sow: 4 *Number of events exceeding 3 days: 57 *Damage function sum calculated by skow: 10.6575 *Damage function sum calculated by sow: 0.00041 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 679 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.4242 *Total damage function for aggriculture: 9.1666 *Total damage for grass: 10905.1028352 *Total damage for aggriculture; 0 *Total damage: 10905.1028352 *Anual avarage risk: 108.973403461863 ----------------------------------------------------------------- 114 ----------------------------------------------------------------*Location: 397 *Water compartment: 399 *Number of events: 210 *Number of events in spring: 15 *Number of events in summer: 22 *Number of events in autumn: 49 *Number of events in winter: 124 *Duration of events in spring: 27 *Duration of events in summer: 34 *Duration of events in autumn: 101 *Duration of events in winter: 231 *Number of events calculated by skow: 210 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 24 *Damage function sum calculated by skow: 11.5137 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 393 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.2348 *Total damage function for aggriculture: 11.4786 *Total damage for grass: 10891.3630644 *Total damage for aggriculture; 269281.4820696 *Total damage: 280172.845134 *Anual avarage risk: 2799.73412018589 --------------------------------------------------------------------------------------------------------------------------------*Location: 403 *Water compartment: 402 *Number of events: 71 *Number of events in spring: 7 *Number of events in summer: 8 *Number of events in autumn: 19 *Number of events in winter: 37 *Duration of events in spring: 12 *Duration of events in summer: 13 *Duration of events in autumn: 29 *Duration of events in winter: 69 *Number of events calculated by skow: 69 *Number of events calculated by sow: 2 *Number of events exceeding 3 days: 4 *Damage function sum calculated by skow: 1.3831 *Damage function sum calculated by sow: 0.00018 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 123 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.0957 *Total damage function for aggriculture: 1.3834 *Total damage for grass: 4343.4540765 *Total damage for aggriculture; 3371.124456 *Total damage: 7714.5785325 *Anual avarage risk: 77.0908712797049 ----------------------------------------------------------------- 115 ----------------------------------------------------------------*Location: 406 *Water compartment: 407 *Number of events: 1422 *Number of events in spring: 277 *Number of events in summer: 175 *Number of events in autumn: 239 *Number of events in winter: 731 *Duration of events in spring: 816 *Duration of events in summer: 483 *Duration of events in autumn: 966 *Duration of events in winter: 4181 *Number of events calculated by skow: 1392 *Number of events calculated by sow: 30 *Number of events exceeding 3 days: 603 *Damage function sum calculated by skow: 17.938 *Damage function sum calculated by sow: 0.00464 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 6446 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 2.3168 *Total damage function for aggriculture: 17.9429 *Total damage for grass: 109718.076096 *Total damage for aggriculture; 257216.3519688 *Total damage: 366934.4280648 *Anual avarage risk: 3666.73236170542 --------------------------------------------------------------------------------------------------------------------------------*Location: 409 *Water compartment: 411 *Number of events: 1553 *Number of events in spring: 337 *Number of events in summer: 215 *Number of events in autumn: 248 *Number of events in winter: 753 *Duration of events in spring: 1178 *Duration of events in summer: 645 *Duration of events in autumn: 1186 *Duration of events in winter: 5213 *Number of events calculated by skow: 1529 *Number of events calculated by sow: 24 *Number of events exceeding 3 days: 746 *Damage function sum calculated by skow: 23.9591 *Damage function sum calculated by sow: 0.00347 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 8222 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 3.1277 *Total damage function for aggriculture: 23.9624 *Total damage for grass: 154210.873176 *Total damage for aggriculture; 643520.4120576 *Total damage: 797731.2852336 *Anual avarage risk: 7971.63442781208 ----------------------------------------------------------------- 116 ----------------------------------------------------------------*Location: 415 *Water compartment: 414 *Number of events: 288 *Number of events in spring: 29 *Number of events in summer: 8 *Number of events in autumn: 35 *Number of events in winter: 216 *Duration of events in spring: 188 *Duration of events in summer: 39 *Duration of events in autumn: 269 *Duration of events in winter: 1827 *Number of events calculated by skow: 288 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 187 *Damage function sum calculated by skow: 27.0971 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 2323 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.9778 *Total damage function for aggriculture: 23.8066 *Total damage for grass: 27980.67591 *Total damage for aggriculture; 0 *Total damage: 27980.67591 *Anual avarage risk: 279.607586572578 --------------------------------------------------------------------------------------------------------------------------------*Location: 418 *Water compartment: 419 *Number of events: 1394 *Number of events in spring: 343 *Number of events in summer: 183 *Number of events in autumn: 236 *Number of events in winter: 632 *Duration of events in spring: 1532 *Duration of events in summer: 570 *Duration of events in autumn: 1175 *Duration of events in winter: 6852 *Number of events calculated by skow: 1394 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 765 *Damage function sum calculated by skow: 16.869 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 10129 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 1.5844 *Total damage function for aggriculture: 16.8681 *Total damage for grass: 41173.4399724 *Total damage for aggriculture; 0 *Total damage: 41173.4399724 *Anual avarage risk: 411.441318237037 ----------------------------------------------------------------- 117 ----------------------------------------------------------------*Location: 424 *Water compartment: 423 *Number of events: 37 *Number of events in spring: 2 *Number of events in summer: 4 *Number of events in autumn: 10 *Number of events in winter: 21 *Duration of events in spring: 7 *Duration of events in summer: 8 *Duration of events in autumn: 18 *Duration of events in winter: 71 *Number of events calculated by skow: 37 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 6 *Damage function sum calculated by skow: 3.9782 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 104 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.071 *Total damage function for aggriculture: 3.4962 *Total damage for grass: 2568.30075 *Total damage for aggriculture; 44146.5174 *Total damage: 46714.81815 *Anual avarage risk: 466.815655279801 --------------------------------------------------------------------------------------------------------------------------------*Location: 425 *Water compartment: 427 *Number of events: 9 *Number of events in spring: 1 *Number of events in summer: 2 *Number of events in autumn: 2 *Number of events in winter: 4 *Duration of events in spring: 1 *Duration of events in summer: 2 *Duration of events in autumn: 4 *Duration of events in winter: 8 *Number of events calculated by skow: 9 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0.885 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 15 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0.0089 *Total damage function for aggriculture: 0.885 *Total damage for grass: 512.7221025 *Total damage for aggriculture; 9897.309 *Total damage: 10410.0311025 *Anual avarage risk: 104.026210162966 ----------------------------------------------------------------- 118 ----------------------------------------------------------------*Location: 431 *Water compartment: 430 *Number of events: 0 *Number of events in spring: 0 *Number of events in summer: 0 *Number of events in autumn: 0 *Number of events in winter: 0 *Duration of events in spring: 0 *Duration of events in summer: 0 *Duration of events in autumn: 0 *Duration of events in winter: 0 *Number of events calculated by skow: 0 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 0 *Damage function sum calculated by skow: 0 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 0 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 0 *Total damage function for aggriculture: 0 *Total damage for grass: 0 *Total damage for aggriculture; 0 *Total damage: 0 *Anual avarage risk: 0 --------------------------------------------------------------------------------------------------------------------------------*Location: 432 *Water compartment: 434 *Number of events: 1062 *Number of events in spring: 155 *Number of events in summer: 122 *Number of events in autumn: 176 *Number of events in winter: 609 *Duration of events in spring: 451 *Duration of events in summer: 322 *Duration of events in autumn: 690 *Duration of events in winter: 39359 *Number of events calculated by skow: 1062 *Number of events calculated by sow: 0 *Number of events exceeding 3 days: 420 *Damage function sum calculated by skow: 100.6387 *Damage function sum calculated by sow: 0 *Damage function sum calculated due to duration exceeding 3 days: 0 *Total duration above target level: 40822 *Total simulation period in days: 36527 *Total simulation period in years: 100.07397260274 *Total damage function for grass: 2.4686 *Total damage function for aggriculture: 70.5741 *Total damage for grass: 193104.4872312 *Total damage for aggriculture; 0 *Total damage: 193104.4872312 *Anual avarage risk: 1929.67031263724 ----------------------------------------------------------------- 119 5-Statistical information on elevation data of water compartments Comp. 306 312 317 322 325 330 336 337 344 346 352 359 364 367 373 377 383 385 389 395 399 402 407 411 414 419 423 427 430 434 Count 1939.00 1280.00 1331.00 1253.00 1506.00 900.00 427.00 754.00 1142.00 1780.00 922.00 441.00 285.00 409.00 1301.00 1033.00 649.00 786.00 810.00 524.00 1298.00 1048.00 1358.00 1591.00 553.00 638.00 898.00 1243.00 1528.00 1569.00 Area 1211875 800000 831875 783125 941250 562500 266875 471250 713750 1112500 576250 275625 178125 255625 813125 645625 405625 491250 506250 327500 811250 655000 848750 994375 345625 398750 561250 776875 955000 980625 Min -648.00 -604.00 -678.00 -609.00 -674.00 -626.00 -618.00 -607.00 -619.00 -629.00 -598.00 -494.00 -496.00 -603.00 -651.00 -646.00 -620.00 -597.00 -638.00 -576.00 -595.00 -585.00 -553.00 -588.00 -581.00 -495.00 -625.00 -629.00 -636.00 -598.00 Max -161.00 -355.00 487.00 -412.00 1627.00 1583.00 603.00 676.00 -155.00 657.00 993.00 816.00 -105.00 1631.00 1631.00 45.00 895.00 -295.00 287.00 -192.00 -190.00 -192.00 -142.00 -111.00 -26.00 55.00 -191.00 -175.00 -171.00 -194.00 Range 487.00 249.00 1165.00 197.00 2301.00 2209.00 1221.00 1283.00 464.00 1286.00 1591.00 1310.00 391.00 2234.00 2282.00 691.00 1515.00 302.00 925.00 384.00 405.00 393.00 411.00 477.00 555.00 550.00 434.00 454.00 465.00 404.00 Mean -475.83 -486.00 -465.92 -508.63 -249.67 -232.96 -352.23 -397.36 -474.10 -422.29 -132.09 -100.61 -248.87 -123.63 -410.18 -486.85 -376.16 -478.38 -444.25 -451.44 -452.99 -417.80 -270.12 -249.80 -451.30 -267.85 -479.97 -478.97 -499.36 -471.10 Std 61.07 31.97 88.22 19.41 281.77 318.33 232.97 184.11 74.43 128.55 268.27 228.14 47.97 357.03 212.44 89.65 202.04 35.07 81.63 66.70 49.76 69.13 48.10 46.30 94.10 75.20 73.64 69.17 63.62 52.74 Variety 307.00 175.00 261.00 106.00 689.00 572.00 254.00 300.00 253.00 420.00 373.00 266.00 125.00 324.00 437.00 276.00 262.00 152.00 260.00 181.00 225.00 269.00 220.00 220.00 215.00 194.00 237.00 267.00 270.00 249.00 Majority -486.00 -481.00 -481.00 -504.00 -482.00 -505.00 -507.00 -493.00 -486.00 -518.00 -239.00 -233.00 -256.00 -472.00 -508.00 -528.00 -452.00 -472.00 -450.00 -490.00 -487.00 -468.00 -283.00 -233.00 -514.00 -291.00 -530.00 -525.00 -523.00 -478.00 Minority -648.00 -604.00 -678.00 -609.00 -674.00 -626.00 -618.00 -607.00 -619.00 -629.00 -598.00 -494.00 -496.00 -603.00 -651.00 -646.00 -620.00 -597.00 -638.00 -576.00 -595.00 -585.00 -553.00 -588.00 -581.00 -495.00 -613.00 -629.00 -636.00 -598.00 Median -481.00 -485.00 -483.00 -509.00 -344.00 -315.00 -459.00 -483.00 -496.00 -468.00 -223.00 -206.00 -242.00 -238.00 -491.00 -516.00 -447.00 -480.00 -460.00 -474.00 -465.00 -439.00 -264.00 -242.00 -489.00 -286.00 -504.00 -504.00 -517.00 -477.00 120 121