Leseprobe
Table of contents
1 INTRODUCTION
2 LITERATURE
2.1 Peatlands hydrology
2.1.1 Hydrological measures
2.1.2 Hydrological cycle in catchment
2.1.3 Surface water and ground water interactions
2.1.4 Runoff in Peatland and groundwater
2.1.5 Water retention and subsurface flow
2.1.6 Surface and subsurface flow paths
2.2 Runoff components
2.3 Hydrograph recession analysis
2.3.1 Individual Recession Segment (IRS)
2.3.2 Master Recession Curve (MRC)
2.3.3 Wavelet Transformation (WT)
2.3.4 Recession constant and recharge from baseflow separation
2.3.5 Recession constant and storage from specific yield
2.4 Groundwater movement in soil
2.5 Water balance and its uses
2.5.1 Soil moisture balance
3 Materials
3.1 Site Description
3.2 Data preparation
4 Methods
4.1 Hydrograph recession analysis
4.1.1 Individual recession curves
4.1.2 Analysis of master recession curve
4.1.3Wavelet transformation
4.1.4 Recession constant and recharge from baseflow separation
4.1.5 Recession constant and storage from specific yield
4.2 Unsaturated moisture balance components
4.2.1 Soil-water mass balance
4.2.2 Class U3M-1D output
5 Calculations
5.1 Recession constant and recharge from hydrograph analysis
5.1.1 Individual recession segments (IRS)
5.1.2 Master recession curve (MRC)
5.1.3Wavelet transformation
5.1.4 Base flow separation
5.2 Recession constant and storage from specific yield
5.2 Recharge volume from unsaturated water balance
6 Results and discussions
7 Conclusion
8 References
9 Appendices
Abstract
Groundwater plays an important role in feeding springs and streams, supporting wetlands and land surface stability. In Finland, most water is held in the soil than the surface systems. Hence, Finland’s water resources depend on groundwater and biogeochemical processes. The study of groundwater in peatland is important for maintaining ecological balance and conservation of water resources. The groundwater level is one of the key indicators of aquifer conditions and groundwater basins. It helps to interpret hydrogeology, groundwater flow, groundwater sustainability and land usability. The study tries to analyze ground water recharge on peatland catchments using hydrograph recession analysis.
The equation for the hydrograph recession curve can be utilized to predict groundwater recharge during each recession period. The steps involved during recession curve analysis includes selection of analytical expression, derivation of recession characteristic and optimization of the parameters. While computing groundwater recharge with recession curve, the high variability of each recession segments creates major problem. Each segment shows the outflow process which creates short-term or seasonal influence. The variation in rate of recession which causes problems for derivation of recession characteristics. The computer software such as hydro-office, VBA macro excel and Matlab are used for recession analysis. The results obtained do not consider climatic influences. The results werethen confirmed by using water balance model and statistical tests. The e-water toolkit is used for water balance model and statistical tests are performed using R-software.
The rainfall-runoff data are used as input to the software used in each method. From the analysis,required output recession parameters are obtained for further calculation. These estimated recession parameters can be used to predict low flows (groundwater contribution to runoff) to understand catchment groundwater resources and as inputs for the rainfall-runoff model analysis. Hence, the objective of this thesis is to analyze groundwater recharge by studying the recession limb of the runoff hydrograph. The thesis workcompares various recession analysis methods. It also tries to identify the better method by comparing groundwater recharge from different methods with groundwater recharge from unsaturated water balance model. Furthermore,the recession constants obtained from different methods are compared with the theoretical values. Statistical tests are used to identify the best method among recession analysis methods used in this study.
Additional information
Acknowledgement
This thesis is written as completion to Master’s Degree in Programme (BCBU) in Environmental Engineering, at university of Oulu, Finland. The intent of this thesis is to study surface and underground hydrology of Peatland catchment. This thesis work is funded by university of Oulu (Water Resource and Environmental Laboratory) and MVTT (Maa-ja Vesitekniikan Tuki). I want to express my gratitude to university of Oulu and MVTT for generous financial support.
I will be forever grateful to Professor Björn Klöve (Director, Water Resource and Environmental Engineering Laboratory, University of Oulu), Anna-Kaisa Ronkanen, and Meseret Menberu for their continues help and support. I would to like express my huge thank you to all of them for never letting me down with precious help and support. I would also like to thank Metsähallitus, Jouni Penttinen and my advisor Meseret Menberu for providing required data and catchment information.
Besides, I would like to thank all my friends and family who have supported me all the time.
Rajib Maharjan
August 2014
Abbreviations
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1 INTRODUCTION
Peatlands are major important part of global ecosystem. It shows significant interaction with natural hydrological system, biogeochemical cycling and terrestrial as well as aquatic biodiversity. In Finland, peatlands have high influence in ecological as well as socio-economic aspects. It covers one-third of Finnish land area which is 2.0 million ha of 9.3 million ha (Virtanen and Valpola, 2011). The hydrological study is used to develop the functions and process related peatlands system.Hydrological study is an important part of environmental and ecological study in Finland. The study of hydrological behavior in surface and subsurface of two peatlands catchment is the major objective of this thesis.
In peatlands as in other soil formation there is interactive connection between the surface and subsurface hydrological water system. This study intends to calculate yearly groundwater recharge of two catchments using recession hydrograph. It includes study of various hydrograph recession analysis methods. It also includes various climatic factors that influence runoff hydrograph.The amount of water received by catchment is disintegrated in different time period. The hydrological features of catchment influences runoff and water storage in the catchment.The runoff generated is highly influenced by upslope contributions from surface flow as well as interflow. In peatlands water storage is high due to different in hydraulic conductivity and pore density (Labadz et al., 2010) . The upper layer acrotelm consists of newly formed peat which has high hydraulic conductivity and limited storage capacity. The lower layer catotelm consists of compressed decompositions which remains permanently saturated resulting in low hydraulic conductivity. Due to unique hydrological surface condition, it is also highly affected by climatic factors (Labadz et al., 2010) .The hydrology of catchment depends on its location and climatic features.
The runoff data obtained is used to draw hydrograph. It consists of various flow components. The recession limb of the hydrograph can be analyzed to study changes in catchment characteristics.Recession analysis method has been used successfully in many catchments for various purposes such as flow predictions, low flow probabilities and groundwater storage calculations (Price, 2011). In this study, the hydrograph recession analysis is carried out using several methods: individual recession analysis, master recession analysis, wavelet transformation, baseflow separation and also by using specific yield. Wavelet transformation is only used for calculation of recession constant. Fromother methods,numerical quantities can be obtained whereas wavelet analysis is effective in visual quantification. The software programs used in this study are Hydro-office software (Hydro Office, 2011) , VBA macro excel spread sheet (Kristijan et al., 2006), Matlab and Baseflow program ( Morawietz, 2007) . The groundwater recharge volumes calculated from recession analysis and specific yield were verified by applying unsaturated water balance model. The unsaturated moisture balance is carried out with Class-1D unsaturated moisture movement model (E-water toolkit, 2000). It is a physical based eco-hydrological modeling tool. The objective of the thesis is to thoroughly study groundwater recharge using hydrograph recession methods. Furthermore, the groundwater recharges obtained from different methods are compared with groundwater recharge from unsaturated water balance model using statistical approach.
2 LITERATURE
2.1 Peatlands hydrology
Peatlands are the area consisting peat layers. They are formed by partially decomposed dead plants in the waterlogged conditions with reduced amount of oxygen in the soil. Peatlands store large amount of water which help in stream flow during dry seasons. It also contributes in the attenuation of flood peaks by preventing flood damages in downstream areas (Querner et al., 2009). Peatlands requires persistent long term water sources. The major sources of water are precipitation, surface runoff during rainfall or snowmelt, water bodies nearby, groundwater or combination of these sources. The sources of water loss from the peatlands are evapotranspiration, transpiration of plants and surface water or groundwater flow (Anderson and Samargo,2007).
2.1.1 Hydrological measures
The peatlands behavior can be defined by three hydrological behaviors such as water level, hydro pattern and residence time(EPA, 2008). The water level in peatlands is related to soil surface.It contains large areas of exposed, saturated soil covered with macrophytic vegetation. So, water level can be used as indicator for the existence of different vegetation in various types of soil zones. The hydrological pattern is dependent on the net difference between inflows and outflows from various water systems. It determines temporal variability of water levels. The hydrological pattern in peatlands involves timing, duration and distribution of water levels(Chaubey and Ward,2006). The hydrological system in peatlands is more static which may not show short-term or long-term variations. But some hydrological systems such as tidal marshes show fluctuation in short time period whereas some may fluctuate more slowly over time. Another measure for peatlands hydrology is residence time or travel time of water through peatlands (Belyea and Nilsmalmer, 2004). The residence time is the ratio of volume of water to the duration of water flow through peatlands. The exchanges of water in some peatlands are very fast resulting in short residence period whereas in some peatlands the flow is slow thereby creating long residence period. The short residence time occurs when the flow through the peatland is large compared to the volume of flow. The long residence time occurs when the flow through the peatland is small as compared to the volume of flow. The residence time explains the water loss from the hydrological system in peatlands (EPA, 2008).
2.1.2 Hydrological cycle in catchment
A catchment can also be studied as an individual hydrological system. The major water source for any catchment is rainfall and some external sources such as irrigation (Thorsten et al., 2007). The incoming water is converted to infiltration, overland flow and some as interception storage. The water from overland flow is the combination of surface runoff and interflow. It travels to runoff points through some flow channels. The infiltrated water is stored by soil as unsaturated moisture (Wang et al., 2009). The infiltrated water contributes to interflow and groundwater storage. The accumulated storage contributes to the surface runoff. The evaporation losses at various stages and runoff are the out flow sources for the catchment. So, a catchment can be considered an individual hydrological system where incoming and outgoing water fluxes are balanced (Kuchment et al., 2011).
2.1.3 Surface water and ground water interactions
Surface water and groundwater interaction depends on various geological features and viability of water pressure (National Water Commission, 2012). In peatland, the interconnection of surface water and groundwater occurs in three different ways: Inflow from bed, outflow from bed and both inflow and outflow from other places (Water, 2011). The water runoff from Peatland can be the rapid drainage of water from land surface or in similar way by which lakes and rivers receive water. Generally, the peatland formed in depressed land surface interacts as streams and lakes. Peatlands formed in slopes and drainage divides received water from groundwater flow from up slopes and precipitation (Tfaily, 2011). In peatland there is also surface water and upper zone soil interaction. The soil contains layers in which top layer is fibrous root mat which high hydraulic conductivity. Upper soil zone contains sufficient interaction between surface water and upper soil. The lower layer is fine-grained soil. It contains highly decomposed sediments which makes the process of water and solute transfer between surfacewater and ground water much slower (Brown etal., 2011)
2.1.4 Runoff in Peatland and groundwater
Runoff is flow of water from the catchment. It can be described as overland flow and subsurface flow. Infiltration excess, saturation excess and returnflows occur as overland flows. Subsurface flow occurs as preferential flow, subsurface flow, and groundwater (Linard, 2009). The runoff generation process describes various water entering mechanisms such as rainfall, snowmelt, soil and ground water movements (Koivusalo, 2002). Runoff shows all the processes influencing hydrologic cycle. It helps to understand the hydrological phenomena in catchments. Runoff can also be considered as good indicators of groundwater storage, water level fluctuation and groundwater contribution to peatlands (Bay, 1968).The interaction between groundwater and peatlands is determined by the hydrological setting of the area. Most peatlands depend on groundwater and is effected by drainage, climate, groundwater use or land uses. Also peatlands are often aquitards which control groundwater runoff (Klöve, 2008).In most peatlands groundwater table not only depends on precipitation-evaporation relations but also on water table in channels and streams. The groundwater recharge occurs when head gradients produces flow from the surface to deeper peat. The head gradients also indicate flow from the deeper peat towards surface (Fraser et al., 2001). Groundwater supports for the stability of peatlands by ingesting water. There is an excess water in surface supportingrunoff during dry periods. In peatlands groundwater also provides ecologically important services such as thermal, temporal and chemical buffering, aquatic ecosystem and plant diversity etc. (Kløve et al., 2013). In peatlands, the surface features are dependent on ground water. The groundwater dependence can be classified according to the response of surface ecosystem. The changes in groundwater can be entirely dependent, highly dependent, proportionally dependent, facultative dependence and no dependence on catchment ecosystem (Barrow,2010).
2.1.5 Water retention and subsurface flow
The moisture content in peat soil is usually very high ranging from 600-1800% compared to dry mass of dry material in the same volume (Labadz et al., 2010). According to Darcy’s law, water flow through a unit area of wet peat is determined by the hydraulic conductivity of material and its hydraulic gradient. Generally, it has low hydraulic conductivity and high water retention capacity even in high hydraulic gradient (Miyazaki,2006). The velocity of water flow through peat is also widely dependent on its physical properties. The properties influencing flow are vegetation composition, compaction, decomposition and presence of micro pores and entrapped gas bubbles (Thompson, 2004). Peat bog can be defined as diplotelmic substance. It contains an upper layer consisting roots and recent decomposing plants known as acrotelm. The lower layer consists denser and more decomposed humified peat known as catotelm (Water, 2010). In general condition, acrotelm has less thickness, higher hydraulic conductivity and limited storage capacity. Catotelm is denser due to continuous deposits from acrotelm and less hydraulic conductivity. This ensures storage of large amount of water in peat bogs and poor water supply to streams by means of base flow. It also helps to maintain favorable conditions for continuing surface vegetation (Labadz et al., 2010).
2.1.6 Surface and subsurface flow paths
The water flow regime in peatland shows two different flow paths during wet and dry period (Andradottir, 2010). The flow is mainly defined by water head and pore water chemistry between interacting surfaces. Two distinct recharge and runoff zones can be obtained as it is influenced by local groundwater as shown in Fig. (1). During base flow, a small amount of water is contributed by hill slopes. It results in small runoff but in wet condition, additional overland flow path is obtained (Fitzgerald et al., 2003). In dry conditions only small runoff are obtained. Also the response times and runoff recession are shorter. In wet condition there is more hydrological coupling between upslope and down slope. It causes complete saturation of hill slope and peat slope(Ballantyne, 2004). The interference zone receives sufficient runoff through open fen and littoral zones. The response time for groundwater flow in deeper peat with low hydraulic conductivity in dry period is longer. During wet period it can be seen with few days of major rainfall(Branfireun and Roulet, 1998).
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Figure 1: Surface and sub-surface flow paths in a catchment (Michigan Technological University 2009).
2.2 Runoff components
The runoffobtained from the catchment can be explained by hydrograph components. The components can explain the time and process of runoff process (Kuchment,2004). Precipitation is source of water for the catchment. The precipitation captured by catchment is later divided into different flow components. The water flow is divided into various components as per time and location. As water passes through catchment it travels through different soil surface and soil layers. The water flow through surface is called surface flow (DeKeyser, 2006). The remaining water infiltrates through surface to form base flow. The time period of surface flow in most cases is shorter than that of base flow. Base flow is further divided as delay interflow and groundwater runoff (Ramírez, 2000). The runoff in various stages involves various hydrological processes. The process includes saturated overland flow, rapid subsurface flow through macro pores and root channel and slow lateral surface flow in saturated areas (Peters, 2013).
A hydrograph is a graph showing the rate of change of runoff with time. It shows how the catchment responds to the rainfall event. Generally, there is a gradual decrease in the flow rate before the beginning of rainfall (National research council, 2008). After rainfall the flow rate increases at first and gradually decreases with time. Hydrographs contains various flow components associated with different time of flow. The components of hydrograph are quick flow, inter flow and base flow as shown in Fig.(2). It also defines time periods for different types of flow. The shape of hydrograph depends on shape, size, slope, elevation and other basin characteristics (Lastoria, 2008). Also the shape of hydrograph varies with land use, surface cover, soil type, geological conditions and channel characteristics.
Generally, hydrograph contains three segmentsas per various flow rates: rising limb, crest segment and recession limb. The rising limb is also called concentration curve. It indicates runoff due to gradual increase of storage in the catchment (Creed and Band,1998). Rainfall increases runoff and decreases infiltration losses in time. Hence, the catchment shows gradual rise in runoff during rainfall events. The crest segment indicates the maximum runoff in outlet (Habets et al., 2010). It occurs after some duration of rainfall depending on the basin and rainfall characteristics.Also the occurrence is appeared when the runoff from different parts of catchment contribute to outflow. The recession limb represents the flow which occurs when the storage capacity of catchment exceeds the maximum capacity. It entirely depends on basin characteristics and storage characteristics of the catchment (Vitvaret etal., 2002).
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Figure 2 : Hydrograph with its components (Ghelardi, 2011).
The hydro graph also contains raising limb which indicates the flow rise after some duration of rainfall. The lag time (tr) defines the time difference between peak rainfall and peak runoff. The time of concentration (tc) is the time period required for the flow due to rainfall to reach runoff charge point due. The falling limb defines the recession flow. It contains information about different flow such as interflow and base flow. The base flow after inflection point is mostly dominated by groundwater flow (Han, 2010).
2.3 Hydrograph recession analysis
A recession hydrograph is a part of hydrograph showing decrease of runoff rate after rainfall or snow melt. The recession part in hydrograph is independent of rainfall characteristics. It indicates the water flow to the outlet event after hours of rainfall event (Knapp, 1979). It depends on the basin characteristics and entirely represents the basin storage capability. The starting point of recession limb of hydrograph is called inflection point. The starting point or point of inflection represents the maximum storage which includes surface storage, interflow storage and groundwater storage (Granato, 2012).
There is change in slope of recession hydrograph as the flow changes. Initially, there is steep slope. The flow is dominated by flood flow component which gradually decreases when flow component is dominated by subsurface flow. The curve shows similar behavior till the end of recession period.In the condition of subsequent rainfall, the curve rises indicating the increase of flow. So, the runoff in outlet during recession period is dominated by flow from natural groundwater storages (Natural Heritage Institute, 2003). To understand runoff process and groundwater flow components such as interflow, shallow groundwater flow and deep groundwater flow, the analysis of recession curve can be carried out. For analysis, the recession segments can be selected from hydrograph. The selected segments can be analyzed individually or collectively (Eylon et al., 2006). The recession curve indicates water from surface storage, subsurface flow and groundwater flow. The recession curves can be analyzed as an exponential segment representing the depletion of a reservoir. The rate of depletion of reservoir is represented by recession co-efficient (α) (Martins, 2007). The equation showing relation of runoff with time is shown in equation (1):
(1)
Where Qt = runoff at time t after flow Qo
Qo = intial runoff at time to
k = e-α= recession constant
The recession hydrograph represents surface flow, inter flow and groundwater flow. The recession constant can be defined as the product of three components as per equation (2) (Subramanya, 2008).
(2)
Where ks = recession constant during surface flow
ki = recession constant during interflow flow
kg= recession constant during groundwater flow
The recession parameters can be used for quantifying various hydrological processes. The most common application in which the recession parameters is used are low flow forecasting, estimation of groundwater resource of the catchment, rainfall-runoff models and hydrograph analysis(Matonse and Kroll,2009). Hydrograph recession analysis can be carried out in using the semi-logarithmic plot of a single hydrograph segments, master recession, relative new approach based on wavelet transformation and baseflow separation (Sujono et al.,2004). The methods for recession analysis can be described as below:
2.3.1 Individual Recession Segment(IRS)
The hydrograph recession analysis can be carried out with cumulative analysis of individual recession segments in a hydrograph(Yarnell et al., 2013). The flow during recession period consists of runoff from different sources in a catchment. These sources are considered to be in exponential term. It is based on the concept that the change in slope indicates decreasing contribution of surface and interflow to the runoff. The hydrograph recession consists of three storage flow in which the time concentration for base flow is much higher than surface flow and inter flow (Focus, 2001). The recession constant is calculatedusing the recession slope obtained from flow hydrograph. Recession constant is calculated as an exponential function of the recession slope (i.e. e-α= k). In this method, each individual recession segment or the ratio of runoff value (Qo/Qt) of individual recession segment are plotted in semi logarithmic scale(Commonwealth of Australia, 2006). In time series hydrograph the increase in magnitude of slope represents the increase in surface flow and inter flow. Similarly, when the flow is plotted in semi logarithmic scale the slope obtained represents base flow (Anderson and Burt,1980). Various experiments by researchers proved that change in slope in recession flow is directly related with base flow. Usually, while plotting recession segments, a straight line cannot be obtained. This is due to the fact that recession flow is composed of different flow components (Szilagyi, 1999).
2.3.2 Master Recession Curve (MRC)
The calculation of recession constant from single recession segments shows high variability. To overcome this problem a single master recession curve from each recession curve can be drawn. A master recession curve can be defined as envelope of various recession curves (Sujono et al., 2004). The Master Recession Curve (MRC) represents the mean flow recession rate. The MRC curve is derived from simple exponential decay of flow. The flow hydrograph may also contain information of sudden decline which cannot be considered by MRC (Ramírez et al., 2002). Analysis of recession curve using MRC involved various methods: (a) co-relation method, (b) matching strip method and (c) tabulation method.
a) Correlation method
In this method a fixed time period for is computed from current flow and previous flow measured at certain time t. The procedure is applied for all recession periods. An envelope line is drawn from origin and recession constant(Ritzema, 1994). The equation (3)for calculation recession is shown below:
(3)
Where k = function of slope of correlation line
t = lag time
b) Matching strip method
Matching strip method is similar to semi logarithmic plot for individual recession segments. In this method all the recession segments are plotted in semi logarithmic scale(David, 2010). The recession segments are super imposed and horizontally adjusted until all the recession curve overlap to form a single curve. The master recession curve is drawn with visual estimate and slope of the mean line gives recession parameter k (Strang, 1964).
c) Tabulation method
In this method master recession curve is derived from multiple recession curves. The starting value of each recession curve is chosen and the highest starting value of becomes starting value for the master recession curve (Stewart, 2014). The other recession curves are combined with master recession curve in the descending order of the starting value of each segment. The resulting curve gives a master recession curve. The process of constructing master recession curve is either analytical or computational (Strang, 1964).
2.3.3 Wavelet Transformation (WT)
Wavelet transformation is an accurate way of the separation of signal characteristics in both time and frequencies simultaneously. It is the recent method which is used for analyzing temporal and spatial climate variability. It is implemented in the geophysical signal identifying transient features and quantifying the temporal variability of stream flow and flood hydrograph (Careyn et al., 2013). The main purpose of wavelet analysis for frequency-time domain signal is to identify any change in signal in time. As in signal, wavelet transformation method can be used for identifying any change in hydrological characteristics (Sujono et al., 2004). In this method the time series data is processed as frequency signal. In Fourier analysis the signal as imposed by its corresponding frequencies extended over time -∞ to +∞. But the time series data are defined by certain time frame which is lost in Fourier transformation. The wavelet transformations overcomes this defect. It breaks down signal into constituent parts and produces location in both time and frequency. The process of wavelet transformation of time-frequency domain signal includes wavelet decomposition and presentation in mean square maps (Gurley and Kareem,1999). The decomposition of an arbitrary signal is decomposed to infinite summation of wavelets according to wavelet expansion. During the analysis of discrete time series, wavelet function are wrapped around time interval independent variable t over signal duration T. The equation for wavelet decomposition is shown in equation (4) (George, 1997):
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The signal behavior is analyzed by mean square values of the signal. The mean square values are computed by squaring discrete time series function and integrating over the interval of 0≤x<1. As in signal, the change in hydrograph can be analyzed by wavelet transformation. The recession hydrograph consists of different flow components such as surface flow and base flow. There is certain change in frequency and location when the flow component changed. In hydrograph, base flow component has longest time so it has lowest frequency which is known as cut-off frequency (fc) (Palmroth et al., 2010). The location and frequency value can be computed by observing wavelet maps or by calculating centered frequency. The centered frequency of frequency level is computed as shown in equation (5) (Williams, 2004):-
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2.3.4Recession constant and recharge from baseflow separation
Baseflow represents the part of flow draining to groundwater. It is an important part of basin hydrology. It inflects groundwater system dependence in climate and geography of basin (Qian et al., 2012). Baseflow is part of flow obtained from groundwater and water infiltrated subsurface flow. The amount of base flow depends on the area of drainage, catchment soil properties and base flow index. Base flow index defines the amount of water as surface flow and groundwater flow. It suggests the percentage of groundwater and delayed subsurface in water runoff by the catchment (Ahiablame et al., 2012). The baseflow recession constant denotes the rate by which flow decreases. It is applicable for short term variations in flow. The short term recession rates depend on precipitation and evapotranspiration. The potential base flow supply by infiltrated precipitation depends on baseflow index and its recession rate(Bako and owoade,1988).
2.3.5 Recession constant and storage from specific yield
Specific yield is the total amount of water drained to the groundwater storage in the influence of gravity. The value of specific yield is determined by groundwater storage change in catchment and change in groundwater level (Hilberts et al., 2005).The average groundwater depletion and average storage calculated from the recession method is compared to verify the correctness of the recession analysis method. The specific yield in groundwater system can be calculated as the ratio change is groundwater volume per unit area to change in groundwater table elevation.The equation of the specific yield used for calculation is shown below as equation (7) (Gehamn et al., 2009):
(7)
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The well hydrograph from ground water table also represents slope off recession curve. In similar catchment there is similar behavior in groundwater hydrograph and flow hydrograph. So, the equation of recession curve in flow hydrograph can also be used for groundwater level. The equation can only be applied to dry season. During dry season the water stored in catchment is removed by groundwater drainage and also due to evapotranspiration (Raghavendran, 2013) .
2.4 Groundwater movement in soil
The movement of watertakes place from higher elevation to lower elevation or high pressure zones to low pressure zones. The high elevation or high pressure zones can be termed as recharge areas. In recharge areas water accumulates from various sources resulting high hydraulic pressure head (Biggs, 2012). The low elevation or low pressure zones can be termed as runoff areas. In runoff areas water flow to the low hydraulic pressure heads through an outlet or any other medium. The water movement is mostly downward and sideways. The vertical movement is due to gravity and capillary forces (Eagleson, 1978). The capillary force results in rise of water in soil. In absence of capillary action gravity pulls water downward. The rate of movement depends on adhesion and cohesion. The water molecules are attracted to the solid surface which is known as adhesion. The attraction of water molecules with each other is known as cohesion. In multilayered soil,when the 1st layer is fully saturated, water moves from 1st layer to 2ndlayer (Meixler, 1999). The rate and direction of water movement is affected when it travels from one layer to another due to change in pore size and shape of soil material. The pore size and shape of soil material depends on the factors such as texture and structure, organic matter and bulk density (Athavale et al., 1992).
The porosity of soil material defines the maximum volume of water below water table. Porosity can be defined as the sum of specific yield and specific retention. The specific yield is the ratio volume soil that drains out due to gravity to the volume of soil. The specific retention is the ratio of volume water remained in soil to the volume of soil. Specific yield estimates are based on the water available in unsaturated zone (Taboada, 2003). The change in amount of water in unsaturated zone denotes the change in groundwater level. In unsaturated zone all water due to gravitational fall contributes groundwater storage. This fact also relates groundwater level change due to gravity considering unit area (Williams, 2009).
2.5 Water balance and its uses
Water balance model is a tool for analysis of field experiment results. It gives the better information about the hydrological cycle. From water balance model, required management option can be identified (Gathenya, 2007). It is based on the conservation of mass. It is based on change in water content in soil volume. Thewater content at certain period is equal to difference between amount of water added to the soil volume and amount of water withdrawn from it. The main purpose of water balance is to identify the division of water supply into various components (Xu and Singh,1998). Water balance can be conducted to any specific area with emphasis to soil moisture and vegetation. It includes all inflows, outflows and water storage and is based on land surface, groundwater, soil moisture with certain area. The general conceptual of water balance model can be shown as described as (Lindborg et al., 2006):
Inflow = Outflow + storage change
The water balance has many applications. Some of the applications are synthesis of long term record of the catchment, generation of runoff records from un-gauged catchment. It can alsobe used to compare circulation models, forecasting yield and possible hydrological effects with time control, deriving climatic and hydrological classification. Water balance can explain hydrological phenomena with fewer parameters (Xu,2002).Water balance extend the information on each parameter which allows more accurate determination of parameters. It also provides reliable correlation between the parameter values and catchment behavior. It canalso be used for checking whether all flow components are considered quantitatively. Water balance can be regarded asthe model which includes all the hydrological process of the catchment.It helps in the evaluation of the effect of change in its components (Xu and Singh, 1998).
2.5.1 Soil moisture balance
The soil moisture balance accountsthe amount of water added, removed or stored in soil in certain duration of time. Generally soil moisture balance is used to identify whether soil water deficits or exceeds (IAEA, 2008). In soil, water moves through soil pores due to gravity or capillary forces. The rate and direction of water highly depends on the soil layers due to variation in pore size of the soil. In soil water content can be described as gravitational water, bound water and capillary water (Manzoni et al., 2013). Gravitational and bound water is not available for plants. The gravitational flow in macrospores is rapidly drained out through drainage. The bound water is tightly adhered to soil particles and cannot be taken up by roots. Capillary water is the water filled in small spaces of soil particle and easily gets to surface by capillarity force (Hudson, 1994). The soil moisture held in soil is due to surface tension. The study of soil water balance requires knowledge of various saturation zones beneath the earth surface. Unsaturated zone is also known as vadose zone. It lies between land surface and water table.
The saturated zone is also known as phreatic zone. It contains water at greater pressure than atmospheric pressure and the soil pores are completely filled with water (Sumangala, 2011). Water table is the surface dividing saturated and unsaturated zone where pore pressure is equal to atmospheric pressure. Capillary fringe is zone just above water table which is a saturated by capillary forces (Vandewiele et al., 1992). The two types of water balance model can be explained as below:
a) Saturated moisture balance
The water balance in saturated zone is called groundwater balance. The water balance in saturated zone helps to determine the significant components effective ground water regime (Zhang et al., 2002). In this method, all the components relating to inflow and outflow in groundwater system is quantified. Also the equation of groundwater balance can be used for quantifying unknown component which are difficult to quantify from physical methods. The general equation for groundwater balance is shown as equation (8) (Noraly, 2011):
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The amount of water available in saturated zone depends on porosity and permeability of soil material. It is also affected by climatic factor and soil type. The evapotranspiration from shallow stores and leakage are difficult to quantify. They are determined by various modeling methods (Shunjun et al., 2006).
b) Unsaturated moisture balance
Unsaturated zone is also known as vadose zone. This zone acts as interactive medium for the transfer of land surface to groundwater and vice versa. It defines interrelationship between various catchment low parameters (Reilly and Lech, 2007). The study of unsaturated zone helps to examine the process of groundwater flow generation and routing along with groundwater runoff to outlet. It is based on the assumption that at some point beneath soil surface, there is change in hydraulic conductivity of soil from higher to lower soil layer. This fact indicates that all water below that point percolates to groundwater storage. The point that lies just below zone of root water uptake are known as zero flux planes (Wood, 2011). Above this plane there is upward movement of soil moisture due to evaporation. Soil moisture below the zero flux planecontributes to groundwater by process of percolation (Moubarak, 2013). The unsaturated soil layer can hold maximum water capacity of soil. The amount of water stored in unsaturated zone depends on actual evapotranspiration, Percolated groundwater and rate of capillary raise from groundwater. The properties of soil are used to compute water balance parameters (Khire et al., 1997)
The water balance in unsaturated zone can be done with Zero Flux Planes (ZFP) concept. ZFP method is one of the methods for determining soil moisture balance in unsaturated soil. Zero flux planesare an arbitrary layer in unsaturated zone which separates upward and downward movement of water in wetted soil (ISMAR, 2005) . Above this plane evaporation occurs resulting upward movements of water.Below it, downward movement occurs as drainage to the water table. Usually in dry periods evapotranspiration exceeds rainfall. In dry periods soil water in upper part moves upwards to root zone. The soil water in lower depth moves due to gravity as recharge to the ground water table . So, the application of concept is based on an assumptionthat below ZFP,extraction from root zone is negligible. The water infiltrating surface moves downward through soil matrix (Magdi et al., 2003) . ZFP methods can be used for wide applications regarding groundwater studies. It is applicable for many practical problems regarding water, energy and fluxes on land surfaces as well as unsaturated zone. It separates upward soil water by evapotranspiration from downward soil water movement to water table.From this level, pointestimates of potential storage at different soil layers can be quantified. On this basis ground water contribution can be estimated as the change in soil moisture storage below the ZFP (Scanlon,2004) .
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Figure 3: Unsaturated water balance components (Lucas et al., 2012).
Precipitations, evapotranspiration, recharge, saturated excess runoff (water outflow due to super saturation), excessive infiltration runoff (water inflow upslope) and storage change are unsaturated water balance components as shown in Fig. (3). General water balance equation for unsaturated zone is written as in equation (9) (Yeh et al., 2005):
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3 Materials
3.1 Site Description
The two catchments studied in this thesis are Marjasuo and Röyvänsuo. Marjasuo peatland has been drained since 1968 for forestry and was restored in 2011.Röyvänsuo is a pristine peatland located in Isosyöte National park. Both of the study catchments are the part of larger Iijoki catchment (Ronkanen et al. 2010). The catchments lie in northern Finland at Taivalkoski municipality and both are state owned. The geographical locations of the catchments Marjasuo and Röyvänsuo are at 65o48’19.79’’ latitude and 27o48’42.246’’longitude and 65o49’12.213’’ latitude and 27o48’13.978’’ longitude respectively. Marjasuo covers land area of 65ha (0.65km²) and Röyvänsuo 75ha (0.75km²). The two catchments contain almost similar terrestrial and soil formations. Marjasuo has 2.27 ha (3.5%) open water or pond, 30.55 ha (47%) mineral soil, 16.5 ha (25.5%) fen or open mire and 15.6 ha (24%) forested Peatland and paludified forest. Similarly, Röyvänsuo contains 0.5 ha (<1%) open water, 44.25 ha (59%) mineral soil, 18.75 ha (25%) fen (open mire) and 11.25 ha (15%) forested peatland and paludified forest. The map with location of two catchments areshown in Fig. (4).There is complex landscape formation which contains numbers of hills and depression. There are irregularities in the slope in the catchments.The hydrology of catchments is controlled by surface and sub-surface flow water flow and its accumulation. The surface vegetation is open peatlands with small tress, small water bodies and dense covered forest. The soil depth formation is heterogeneous. The whole surface of the catchments is not covered by peatland rather it is dominated by minerals soil. The surface hydraulic conductivity is measured in the field.
For the study of the catchment, tree cover is taken as surface vegetation. The soil layers are homogenous mixture of sand, loam and peat. The field measured averaged and used as input hydraulic conductivity. Also initial soil moisture content is taken as per site measurement. The average hydraulic conductivity for soil layers for Marjasuo and Röyvänsuo is 9.56 x 10-5ms-1(808.74cmd-1) and 1.814 x 10-5 ms-1(148.95cmd-1). The initial soil moisture for both of the catchment is 0.4-0.6. The other inputs for modeling unsaturated movement are land use, climate data and hydraulic parameters. The landuse data are taken from standard values for tree vegetation from user manual (E-water toolkit 2000) . The climate data is calculated from temperature data measured. The hydraulic parameters are adjusted to mixed soil and available data are used such as hydraulic conductivity and porosity.
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Figure 4 :Catchmentlocationma p (Terrain map using Google Maps, Data SIO 2007).
3.2 Data preparation
The data used are runoff, precipitation, hydraulic conductivity, soil depth and temperature taken from 2010 to 2013. The rainfall data is continuously collected by installing tickling bucket in the site. Temperature, runoff and groundwater level is continuously collected by data loggers.
The runoff data is collected using Thomson V-notch weir dimensioned as per site. Runoff for each time step is calculated by using depth of water measured by Thomson-weir method. In this method flow depend on cross section of weir and backward accumulation height and is calculated as shown in equation (10):
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The average specific yield for four year measured at different locations is given in Table 1. The range of specific yield for four year measured to be from 0.2 to 0.55. In this thesis average value of specific yield is used for calculating recession constant and groundwater recharge.
Table 1 : Average specific yield for two catchments
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For unsaturated soil moisture model rainfall, pan evapotranspiration and soil properties are three major inputs. The daily average temperature and monthly solar radiation is used to calculate pan evapotranspiration. The pan evaporation is calculated using Jensen and Haise, 1963 equation. The equationis most suitable method and is verified from various statistical performance criterion and tested results. Theequation (11) is used to calculate pan evaporation from daily temperatures and monthly solar (Jensen and Haise, 1963):
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The daily solar radiation cannot be obtained for the study area. The solar radiation data from Oulu (Table 2) is used since solar radiation doesn’t vary in close locations (Latitude: (65°01'12"N) and Longitude: (25°28'12"E)) ( Gasima, 2005 ).
Table 2: Daily solar radiation Latitude: (65°01'12"N) and Longitude: (25°28'12"E)
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The study areasare located in Northern Finland. It consists of non-uniform land formationwith distributed surface vegetation. The soil contains peat layers along with minerals soil of varied thickness over the catchment area. There are heterogeneous soil layers in the catchment with varied depth and surface topography. The study area also consists of complex landscape with distinct and repeating patterns of hill slopes. According to Geological Survey of Finland (GTK), the average thickness of mixed soil layer in study area is 1.3m (Kimmo and Samu, 2011). The soil layers are divided into three layers as surface, intermediate and bottom with average thickness of 0.2, 0.4 and 0.7 m respectively. The elevation of soil layers are measured by airborne laser scanning data introduced by GTK Finland. The study sites consist of Aapa mires. The peat strata are dominated by remains of Sphagnum and brown mosses and other combinations (Kimmo and Samu, 2011).
4 Methods
The recession constants and groundwater recharge of both sites Marjasuo and Röyvänsuo are computed using the recession analysis method and specific yield method. Hydrograph graphs are drawn from the time series flow data. Recession analysis involves separation of recession curves from hydrograph. The recession curves are analyzed forcalculating recession parameters and groundwater change. The methods used in this study are individual recession segment, master recession curve, wavelength transformation, baseflow separation and specific yield method. From all methods recession constant and groundwater recharge volume are calculated. The wavelet transformation is only used for calculating recession constant. These methods are carried out using four year data values for both catchments. The parameters obtained from water balance model are assumed to be precise with some uncertainties. In this study the groundwater recharge obtained from unsaturated water balance model is considered to be precise. So, the groundwater recharge obtained from recession analysis methods and specific yield are compared to groundwater recharge from unsaturated water balance model. Finally, statistical tests are carried out to observe the significance of the results obtained. The basic approaches used for this study are discussed in the following sections.
4.1 Hydrograph recession analysis
4.1.1 Individualrecession curves
The analysis of individual recession curves is carried out using RC 4.0 tool from hydro office software (Hydro office 2010). By using RC tool, an individual recession segments are separated from runoff hydrograph. The runoff data is the major input and rainfall is optional. An individual recession curve is selected for short time period with small numbers of declining runoff values.In an individual analysis there is different flow constant for the slow and fast runoff. It consists of two linear models. One represents fast flow and the other represents slow flow. For each model, recession curve is divided into two portions (upper and lower).The initial flow and constant (k) are given by user. For the calibration of individual recession curve,a tool called single calibration in hydro office software is used.
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Figure 5: Single recession curve calibration (HydroOffice, 2011).
The samplecalibrationof individual recession curveis done by dividing recession curve into larger upper and smaller bottom part. The upper part and lower part contains individual recession sub regime with two different time flow velocities. The initial parameter or starting flow and recession coefficients are fixed by adjusting values in the boxes by user. The parameters are fixed until the lines coincide with recession curve as shown in the Fig. (5). Input data lies between the highest and lower runoff values. The lines are adjusted to recession curve by adjusting k values.The outputs obtained from the software are initial flow, recession coefficient and recession time days. The output obtained is used to calculate final discharge and groundwater recharge during recession period.
i) Final runoff at time t
The output contains two initial flows and two constants for same time period. The initial flows and recession constants are added to get total flow and total constant for each individual recession curve. From total initial flow and total recession constant final discharge is calculated.The flow at the end of recession period is given by equation (12) (Tallaksen, 1995):
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ii) Change in groundwater recharge
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The calculated value t1 is used to find the groundwater recharge between each recession curve. In this method groundwater change is calculated based on each log cycle. Each individual volume is added to get total groundwater recharge volume. Individual ground water recharge volume in each log cycle is the difference between total potential groundwater runoff at beginning of recession and total groundwater potential at the end of recession.
The volume of groundwater runoff at the beginning and end of recession is given by equation (15) and (16) ( HydroOffice, 2010):
and (15)
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The volume of groundwater recharge is difference between volume at starting and ending of each recession event, which is shown in equation (17) ( HydroOffice, 2010):
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The calculated recharge is converted to daily volume per unit area. The daily recharge volume is calculated as given in equation (18) ( HydroOffice, 2010):
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4.1.2 Analysis of master recession curve
In master recession curve analysis a single curve is obtained representing all individual recession curves. The analysis of master recession curve is carried out by separating each recession segment from yearly hydrograph. The adapted matching strip method is used for construction of master recession curve. In this method each recession segments are adjusted horizontally until they overlap or combine with each other. A visual basic spreadsheet macro is used for master recession analysis. It consists ofdifferent regression model. In this thesis exponentialregression models are used toobtain final master recession curve from all individual recession curves (Posavec et al., 2006).
In VBA excel sheet, each individual recession curve is fitted to an exponential regression model to draw master recession curve. The date and runoff are initial inputs which gives runoff hydrograph. The automated VBA macro is used to separate individual recession and time of recession from hydrograph. The separation of individual recession is carried out with the separation criteria set by flow duration curve. The flow duration curve shows the percentage of time that a given flow rate is equaled or exceeded. The separation criterion of (10-70) % is selected for each year. The high runoff data value are selected as initial runoff exceeds the corresponding runoff values by (10-70) % in an individual recession curve. The process includes the selection of variable length of recession period from runoff data. The separated time is then ranked in descending order from which initial value of recession is obtained. Then the highest flow value are selected along with declining values. It is then plotted in semi-logarithmic scale in decreasing order which gives the equation with two variables x and y. In thesemi-logarithmic plot, x represents time of flow and y represents flow rates. The second highest number gives the second recession. The curve obtained with second highest value is adjusted to the last point value of first recession curve. The adjustment is carried out with segment translation.In segment translation,the time of second recession is shifted to required place along axes till it fit to the end of first recession. The process continues till the last recession curve is combined. Finally a regression line is drawn with the best fitted model criteria. The regression line obtained is called master recession curve. The criteria are based on trend line R2 describing the data which varies from 0-1. The values approaching to 1 are the best fitted models. The data obtained from VBA macro excel sheet are runoff values for each individual recession, time of recession and equation for regression line. From the exponential regression equation recession constant is calculated.From the recession constant, runoff during each recession and time of recession groundwater recharge is calculated. The calculated processes are similar to individual recession analysis.
4.1.3 Wavelet transformation
Wavelet analysis is carried out to find centered frequency from time series runoff data. Hydrograph interflow is relatively faster than baseflow.The runoff is changed to frequency signal. The time of baseflow is longer. As a consequence, signal frequency is reduced. The central frequency is frequency at which there is change in signal behavior.The wavelength transformation of catchments is done using Matlab. The time series runoff data is converted to frequency signals. To obtain frequency signals from time series data Fast Fourier Transformation (FFT) is used. By using FFT the time domain data is decomposed to frequency signals. From the frequency signals center frequency is obtained.To find center frequency a band pass filter criteria called Nyquist rate is used. The Nyquist frequency and Nyquist rate are two different terms. Nyquist frequency is twice the highest frequency in the signal whereas Nyquist rate is used to obtain symmetric signal. The Nyquist rate is obtained from amplitude modulation which converts signals to symmetric signal within maximum amplitude. In this maximum amplitude is taken as 1. From the symmetric frequency signal center frequency is obtained. The centered frequency obtained from wavelet analysis is used to find the recession parameters for the catchment.The equation for calculation of recession parameter k using the centered frequency is shown in equation (19) (Sujono et al., 2004):-
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The wavelength transformation in this study is only used for comparison of recession constant. The process is relatively new and requires further study to relate with groundwater processes. The further calculation requires initial flow and recession period. The calculation of these flow characteristics further study on reconstruction of original signal. The original signals can be obtained from Short Time Fourier Frequency (STFT) transformation but phase angle cannot be regenerated. Due change in phase angle random data is obtained and data obtained is not equal to original data. The Fast Fourier Transformation (FFT) of signal results in randomization of phase. By doing Inverse Fast Fourier Transformation (IFFT) original signal can be regenerate but at random phase. By using this method the frequency at which baseflow occurs is only obtained. It is unableto determine the original runoff and time at which baseflow starts.
4.1.4 Recession constant and recharge from baseflow separation
Baseflow is separated from total flow using smoothed minima technique. Baseflow program is used for baseflow separation.A Baseflow program is VBA excel which is used to separate surface and base flow (Morawietz, 2007). For separation of base flow mean daily flow is divided into non-overlapping blocks of 5 days. The minima value is calculated for each block. The minima value is called central value. The separation criteria for each bock is as 0.9 × central value <original value. The central value gives ordinate for baseflow line. The process is continued to obtain baseflow ordinates from all values. Base flow index is obtained as the ratio of volume of water lying under base flow line to the volume of water below mean daily flow line (Institute of Hydrology, 1980).
The base from index obtained is used to calculate groundwater recharge volume and recession constant. The equation for calculating groundwater recharge volume from baseflow index is shown in equation (20) (Szilagyi,1999).
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The equation for calculating recession constant from baseflow index is shown in equation (21) (Szilagyi et al., 2003):
4.1.5Recession constant and storage from specific yield
The specific yield is related to groundwater table. The specific yield and change in groundwater level is used to calculate recession constant and groundwater recharge. The time series graph of groundwater level data is similarto runoff hydrograph. From the groundwater level data, the depletion curves are selected. The change in groundwater level during each depletion curve is used to calculate recession constants. The recession slope is calculated as the ratio of product of specific yield and time to the change in groundwater level as shown in equation (22). From recession slope recession constant is calculated using equation (23) (Raghavendran,2013).
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For yearly groundwater recharge, the average groundwater level change in each depletion curve and average specific yield is used. The recharge calculation is based on the assumption that percolated water immediately goes to storage. This method is applicable for short recession periods (Crosbie et al., 2005).The calculation of groundwater volume change is shown in equation (24)(Raghavendran, 2013).
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4.2 Unsaturated moisture balance components
The water balance model is used for each year. Thecalculations are carried out with daily data.The water balance model gives yearly groundwater recharge. The outputs obtained from unsaturated moisture balance are rainfall, infiltration, contribution from upslope, total evaporation, recharge and saturated runoff. The groundwater recharge volume obtained as moisture balance output is used to compare the groundwater recharge obtained from different methods used. The outputs from unsaturated balance moisture model are computed using a software toolkit called class U3M-1D. This program uses Richard’s equation for water balance calculation. The equation is applicable for any soil, weather conditions or vegetation type. The software toolkit contains three alternatives for soil hydraulic modeling: Van Genuchten soil hydraulic model, Vogel and Cislerova soil hydraulic model and Brooks and Corey soil hydraulic model.Brooks and Corey soil hydraulic model is chosen in this study. Brooks and Corey soil hydraulic model is chosen due to easy mathematical manipulation and flexibility of program allowing user input hydraulic parameters.
The software calculates transfer of soil moisture in various layers of the soil in all directions. The unsaturated moisture movement model separates the upward soil moisture and downward soil moisture. The soil moisture in upward direction is evaporation and surface runoff. The soil moisture in downward direction is divided in moisture from top and moisture from bottom of each soil layers. The moisture from top is infiltrated runoff. The soil moisture from bottom is recharge to groundwater storage. The recharge volume obtained from unsaturated moisture balance is compared to recharge volume obtained recession analysis methods and specific yield method.
Class 1D-U3M software consists of various steps. First step is to divide the soil layers into three layers. The catchments contain variable soil composition and most of the area is covered with forest. The forest vegetation is considered for the unsaturated moisture movement water balance. The layers are divided according to soil type. The input soil type in software does not have mixed soil type. To adjust soil type in software as per catchment condition soil properties are changed. Each layer is sub-divided into depth of 0.1 m as shown in Fig. (6).
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Figure 6: Division of soil layers for Marjasuo catchment (E-water toolkit, 2000).
The program calculates various components of evaporation by using input pan evaporation. The evapotranspiration depends on surface vegetation. The constant default values for tree vegetation 0.8, 0.85 and 1 is used for light extinction coefficient (k_light), pan evapotranspiration constant (Kpan) and leaf area index (LAI), respectively. By using different constants and pan evaporation,different evaporation components are calculated. The equations (25), (26) and (27) are used to calculate different components of evapotranspiration (Vaze et al., 2004).
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The calculations and outputs steps involved in various time steps are discussed below:
4.2.1 Soil-water mass balance
The local water balance is performed for each layer of soil. For water balance three boundaries conditions are considered. The upper, lower and upslope boundary are three boundary conditions. The water balance is based on Richard’s equation. The equation is derived fromequation for vertical Darcy’s flux. The equation (28) below, shows the vertical water for each soil layer (Narendra et al., 2004):-
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The unsaturated soil moisture flow in unsaturated zone contains various sources and sinks. The equation for flow in unsaturated zone depends on moisture loss by transpiration, evaporation and moisture gain from horizontal slopes. The equation (30)shows flow in unsaturated zone (Narendra et al., 2004).
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For water balance model three boundary conditions are considered. The boundary conditions can be explained as follows:
i) Upper boundary
The upper boundary condition is time dependent specific flux boundary used at the soil surface. The upper boundary flux contains flux infiltrated to soil and flux which cannot infiltrate from upper soil. The flux which do not infiltrate is surface runoff. Total flux infiltrated in upper boundary is given by equation (31) (Narendra et al., 2004):
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ii) Lower boundary
The lower boundary is used to separate the infiltrated runoff and recharge area of the catchment. It includes total infiltrated soil moisture from upper boundary. The infiltrated soil moisture is divided into soil moisture from top of soil layer and bottom of soil layer. The soil moisture from top results in infiltrated runoff. The soil moisture from bottom results in groundwater recharge. The amount of recharge depends on the minimum flux under unit gradient from bottom layer of soil and hydraulic conductivity of soil layer. The equation for the lower boundary with infiltrated runoff is given by equation (33) (Narendra et al., 2004):
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iii) Upslope boundary
The upslope boundary defines horizontal transfer of moisture from upslope soil layer to downslope soil layer. The volume of moisture remained at end of each time step i.e. receiving water from upslope and contribution to lower layer is calculated as equation (35) (Narendra et al., 2004):
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4.2.2 Class U3M-1D output
The soil moisture flow is based on various soil layers and soil material with the each soil layer. The unsaturated moisture movement is computed in each time step. In this the vertical moisture movement and horizontal moisture movement is calculated by numerical simulation in each time step as (t’+Ϩ t). The vertical simulation is carried for short time step t’.After vertical simulation horizontal simulation is carried out for Ϩ t. Soil moisture, hydraulic conductivity and diffusivity is expressed as geometric mean of all corresponding layers. In each time, step soil from uppermost soil layer to deepest soil layer is calculated. The total moisture isreceivedas a rainfall which represents the total volume as inflow. The total inflow to unit soil area is calculated using equation (36). The total moisture received by unit area contributes to overland flow and infiltration of soil moisture. The flux across top resulting overland flow is calculated using equation (37). The total soil moisture infiltrated is calculated using equation (38) (Narendra et al., 2004).
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The infiltrated soil moisture further contributes in infiltrated runoff and groundwater recharge. The flux at bottom of soil layers contributing infiltrated runoff is calculated using equation (39). The total soil moisture contributing recharge to groundwater storage is calculated using equation (40) (Narendra et al., 2004).
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The remaining vertical soil moisture is considered for total evapotranspiration. Moisture accumulated in soil surface and saturated soil are remaining vertical soil moisture.The remaining soil moisture for each time step can be calculated using equation (41) (Narendra et al., 2004):-
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Penman Monteith equation is used to calculate total evapotranspiration from each soil layers. The actual evapotranspiration iscalculated as minimum of total evapotranspiration and total moisture available.The equation (42) shows formula for calculating total evapotranspiration demand (Narendra et al., 2004):
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The outputs obtained from the software are total evaporation (E), saturated runoff (Wdelta), infiltration runoff (Qtop) and infiltration recharge (Qbot). The soil moisture fluxes are separated in upward and downward direction. Total evaporation (E) and saturated runoff (Wdelta) represents upward flow. The total evaporation and saturated runoff lies above arbitrary plane called zero flux plane. The infiltration runoff (Qtop) and infiltration recharge (Qbot) represents downward flow. The infiltration runoffand infiltration recharge lies below zero flux plane.
5 Calculations
5.1 Recession constant and recharge from hydrograph analysis
The recession constants and groundwater recharge are calculated from individual recession, master recession and baseflow separation. From wavelet transformation, only recession constants are calculated. The recession constants are compared to theoretical values. The groundwater recharge obtained from various methods is compared to groundwater recharge from unsaturated water balance model. The obtained results are statistically compared. The calculation of recession constants and groundwater recharge volume from various hydrograph analysis methods can be shown below:
5.1.1 Individual recession segments (IRS)
Fig. (7) and Fig. (8) shows hydrograph with rainfall data. From the hygrograph with rainfall data, the peak runoff and recession curves are obtained.
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Figure 7 : Marjasuo catchment hydrographwith rainfall for year 2010.
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Figure 8 : Röyvänsuo catchment hydrographwith rainfall for year 2010.
The individual recession curves are selected from each hydrograph. The software provides the value of declining runoff in each time step of the recession.It also calculates slope ofrecession curve i.e. recession constant for each selected recession curve. It gives expected number of recession curve from each hydrograph and the duration of recession. The software gives six recession curves yearly hydrograph for four consecutive years in Marjasuo catchment. For Röyvänsuo, six, five, six and seven recession curvesare obtained for the year 2010, 2011, 2012 and 2013, respectively. The example of runoff data for individual recession curve for Marjasuo year 2010 (Table 3) is shown below.
Table 3 : Marjasuo catchment individual recession curve data for year 2010
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The example of runoff data for individual recession curve for Röyvänsuo for year 2010 (Table 4) is shown below.
Table 4 : Röyvänsuo catchment individual recession curve data for year 2010
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The selected curve is used to determine initial runoff for the recession period. The slope of the curve formed by the declining runoff is obtained for each individual recession curves. Fromrecession slope,recession constants are calculated. The initial runoff, recession constant and time of recession period is used to calculate yearly groundwater recharge. The calculation for final runoff at end of recession, time period for single recession cycle, volume at beginning, volume at end and its difference is carried out to get groundwater recharge. The groundwater change obtained from each individual recession is added on yearly basis to get yearly groundwater recharge. The calculation is carried out using equations (12) to (18). The calculation table for individual recession analysis is shown in Appendix 1.The summary of results from individual recession curve analysis (Table 5) showing annual groundwater change for Marjasuo and Röyvänsuois shown below:
Table 5 : Summary of results from individual recession analysis
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5.1.2 Master recession curve (MRC)
VBA macro excel sheet is used for master recession analysis. The number of curves selected for Marjasuo for the years 2010, 2011, 2012 and 2013 are 11, 17, 14 and 15, respectively. The number of curves selected for Röyvänsuo for years 2010, 2011, 2012 and 2013 are 15, 6, 8 and 13, respectively. VBA macro excel sheet separates individual recession curves from hydrograph. The individual curves are combined to form single exponential master recession curve.Master recession curve is obtained using adapted matching strip method. The master curve represents all individual recession curves. The Fig. (9) shows sample master recession curve for Marjasuo for year 2010 and Fig. (10) shows sample master recession curve for Röyvänsuo for year 2010.
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Figure 9 : Marjasuo catchment master recession curve for year 2010.
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Figure 10 : Röyvänsuocatchment master recession curve for year 2010.
The recession curve values, time of recession and master recession curve exponential equation are obtained as output. The exponential master recession equation is used to calculate recession constant. From recession curve values, time of recession and recession constant final runoff at end of recession, time period for single recession cycle, recharge volume at beginning, recharge volume at end and its difference are calculated. The equations (12) to (18) are used in calculations. The calculation table for groundwater recharge using master recession curve for Marjasuo and Röyvänsuo catchment is shown in Appendix 2.
The summary of results from master recession curve analysis (Table 6) showing annual recharge volume and recession constant for Marjasuo and Röyvänsuo is shown below:
Table 6 : Summary of results from master recession analysis
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5.1.3Wavelet transformation
In wavelet analysis, hydrological time series data is transformed into frequency spectrum.The Fast Fourier Transformation (FFT) is used for transformation of time series to frequency. The frequency spectrum is normalized to unit magnitude. From the symmetric frequency spectrum central frequency is obtained. Matlab codes are used for frequency transformation. The transformed frequency spectrum contains real and imaginary part. The real frequency obtained is plotted against its magnitude. The Fig. (11) is sample of frequency spectrum showing different frequency level and Fig. (12) is normalized magnitude with the sample frequency for time series runoff data for Marjasuo for year 2010 is shown below:
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Figure 11: Marjasuo catchment frequency spectrum for year 2010.
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Figure 12: Marjasuo catchment normalized magnitude with sample frequency for year 2010.
The sample of frequency spectrum showing different frequency level Fig. (13) and its normalized magnitude within the sample frequency Fig. (14) for time series runoff data of Röyvänsuo for year 2010 is shown below.
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Figure 12: Röyvänsuocatchment frequency spectrum for year 2010.
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Figure 13: Röyvänsuocatchment normalized magnitude with sample frequency for year 2010.
The calculation of recession coefficient from central frequency (Table 7) for Marjasuo and Röyvänsuois shown below.
Table 7: Calculation of recession constant from wavelet transformation
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5.1.4 Base flow separation
The runoff data for the catchment is the input data for the baseflow flow program. The program separates surface flow and base flow from runoff hydrograph. The base flow separation from the total flow hydrograph Fig. (15) and Fig. (16) for Marjasuo for year 2010 and Röyvänsuo for year 2010 respectively are shown as follows.
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Figure 14: Marjasuo catchment baseflow separationfor year 2010.
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Figure 15: Röyvänsuo catchment baseflow separation for year 2010.
Base flow index is obtained from base flow and surface flow during baseflow period. From base flow index groundwater recharge is calculated. The equation (20) is used for calculation of recharge volume. The recession constant is calculated using relation between baseflow index and recession constant. The equation (21) is used for calculation of recession constant. The calculation of groundwater recharge volume and recession constant (Table 8 and Table 9) using from results baseflow program is shown as follows.
Table 8: Calculation of recharge and recession constant from baseflow for Marjasuo catchment
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Table 9: Calculation of recharge and recession constant from baseflow for Röyvänsuo catchment
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5.2 Recession constant and storage from specific yield
The groundwater depletion curves are selected from groundwater level data. The number of depletion curves selected for Marjasuo for years 2010, 2011, 2012 and 2013 are 11, 17, 14 and 15, respectively. The number of depletion curves selected for Röyvänsuo for years 2010, 2011, 2012 and 2013 are 6, 5, 6 and 7, respectively. The average groundwater level change is calculated for each depletion curve. The recession slope for each depletion curve is calculated using equation (22). The average value of specific yield is taken from Table (1).The recession slope and groundwater levels from each depletion curve are averaged to calculate yearly recession constant and groundwater recharge. The calculation sample of average recession slope and groundwater level for Marjasuofor year 2010 and Röyvänsuofor year 2010 is shown in Appendix 3. From the value obtained, recession constant and groundwater change (Table 10) are calculated using equation (23) and (24).
Table 10: Recession constant and groundwater change for Marjasuo and Röyvänsuo catchments
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5.2 Recharge volume from unsaturated water balance
The output fluxes are the components of unsaturated water balance model. The output flux contains rainfall (R), total evaporation (E), saturated runoff (Wdelta), infiltration from soil surface (Qtop) and infiltration recharge (Qbot). All the obtained results are in meter per day (m/d).The output fluxesare summed up to get annual values of allcomponents. From results obtained, groundwater recharge volume is separated. The results obtained with all output fluxes in meter per day (m/d) and output soil moistureis shown as Appendix 4. The outputs fromunsaturated soil moisture balance are applicable for various hydrological processes. The components from unsaturated water balance are considered to be precise with some uncertainty. So, the recharge volume from soil moisture water balance is compared with groundwater recharge obtained from other methods. From yearly water balance,components for each year (Table 11) and (Table 12)recharge volume is used for comparison. The negative sign in Tables (11) and (12) indicates downward movement of soil moisture
Table 11: Soil moisture balance components for Marjasuo catchment
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Table 12: Soil moisture balance components for Röyvänsuo catchment
6 Results and discussions
The summary of the results for Marjasuo (Table 13) and Röyvänsuo (Table 14) obtained from hydrograph recession methods and specific yield are shown below.
Table 13: Summary of the recharge volume and recession constant calculated from various methods for Marjasuo catchment
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Table 14: Summary of the recharge volume and recession constant calculated from various methods for Röyvänsuo catchment
Analyzing the results obtained from hydrograph recession analysis and specific yield, best method is identified. The most efficient method is determined from the following two means: a) box plots of recession constants and recharge volume b) statistical significance of different methods with unsaturated water balance method.
The box plots for recession constants Fig. (16) and Fig. (18) shows the plot of recession constants from different methods for two catchments. The plot obtained is compared to theoretical value which lies in between 0.85 to 0.99 (Subramanya, 2008).The box plot for groundwater recharge volume Fig. (17) and Fig. (19) contains groundwater recharge from different methods and also groundwater recharge from unsaturated water balance.
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Figure 16: Box plot for recession constants for Marjasuo catchment.
(In Fig. (16): BK = Base flow recession constant, IK = Individual recession constant, MK = Master recession constant, WK = Wavelet constant and SK = Specific yield constant.)
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Figure 17: Box plot for Groundwater recharge for Marjasuo catchment.
(In Fig. (17): IR = Recharge volume from Individual recession, MR = Recharge volume from Master recession,BR = Recharge volume from Base flow, SS = Recharge volume from specific yield and WR = Recharge volume from water balance.)
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Figure 18: Box plot for recession constants for Röyvänsuo catchment.
(In Fig. (18): IK = Individual recession constant, MK = Master recession constant WK = Wavelet constant, BK = Base flow recession constant and SK = recession constant from specific yield.)
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Figure 19: Box plot for Groundwater recharge for Röyvänsuo catchment.
(In Fig. (19): IS = Recharge volume from Individual recession, MS = Recharge volume from Master recession, BS = Recharge volume from Base flow, BS = Recharge volume from specific yield method and WR = Recharge volume from water balance.)
The theoretical value for groundwater recession lies in the range of 0.85 to 0.99 (Subramanya , 2008).The box plot of recession constants for Marjasuo Fig. (16) andbox plot of recession constants for Röyvänsuo Fig.(18) shows the calculated result of recession constants.Both the catchment shows that the wavelet transformation and baseflow lies in range of theoretical values. The box plot of recharge volume for Marjasuo Fig. (18) and box plot of recharge for Röyvänsuo Fig. (20) shows the calculated result of ground water recharge. Both the catchment shows that groundwater recharge volume calculated from Individual recession and Master recession are close to the recharge values calculated from water balance method. In study wavelet transformation method is used for calculating recession constants only. The recharge volume from baseflow method is not close to recharge calculated from Water balance. The recession constants calculated from Master recession nearly lies in range of theoretical value. Also recharge volume from Master recession is close to recharge calculated from Water balance.
Furthermore, statistical comparison are done using t-test and ANOVA test. Groundwater recharge calculated from different methods is compared to recharge from unsaturated water balance method. The t-test is based on difference between sample means. In t-test, t-values are converted into probability (i.e. P-value). The results of the t- test for two catchments (Table 15 and Table 16) show the statistical significance of recharge from various methods.
Table 15: t-test results for Marjasuo catchment
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For Marjasuo, P-value formeangroundwater recharge from water balance and mean groundwater recharge from individual recession is 0.5085 (i.e. 50.85 % probability that difference between them is 0). Similarly, P-value formean groundwater recharge from water balance and mean groundwater recharges from master recession, base flow and specific yield method are 0.5084, 0.0496 and 0.3272, respectively. For Röyvänsuo, P-value for mean groundwater recharge from water balance and mean groundwater recharge from individual recession is 0.4775 (i.e. 47.75% probability that difference between them is 0). Similarly, P-value for mean groundwater recharge from water balance and mean groundwater recharges from master recession, base flow and specific yield method are 0.505, 0.5398 and 0.4935, respectively.
ANOVA is based on the variability of standard deviation in two variables. If the standard deviation is different, then variables are different regardless of difference in mean values of the variables. The higher P-value shows higher divergence in mean values. The P-values in one way ANOVA test resultis shown in (Table 17 and Table 18). It shows how the mean recharge values from different methods are deviated from the mean recharge values from unsaturated water balance.
Table 17: ANOVA test results for Marjasuo catchment
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In ANOVA test, the results are explained by F-statistics and its corresponding P- values. For Marjasuo,three methods: individual recession, master recession and specific yield method are statistically significant (<0.05). Among all the methods master recession hasthe highest F value (6061) and corresponding lowest P-value (0.000165). For Röyvänsuo, three methods: individual recession, master recession and specific yield method are statistically significant (<0.05). Among all the methods master recession has highest F value (139.4) and corresponding lowest P-value (0.0071).
Finally, from the comparison of recession constant and groundwater recharge from box plots and two test methods, master recession is the most efficient methods among all the methods applied in study. Fromwavelet transformation,groundwater recharge cannot be calculated.Also baseflow method,recession constants are close to the theoretical values but it has high difference recharge volume. From the study of boththe catchments, master recession has recession constants close to the theoretical value. Also, groundwater from this method is close to the groundwater recharge from unsaturated water balance. T-test and ANOVA test shows recharge from master recession and recharge from unsaturated water balance have no significant difference.
7 Conclusion
The study is based on comparison of different methods for calculation of recession constant and groundwater rechargeusing hydrograph recession analysis. Hydrograph recession analysis of catchments Marjasuo and Röyvänsuo is carried out with runoff data. Different recession analysis methods: individual recession, master recession, wavelet transformation and baseflow separation are used to compute recession constant and groundwater recharge. Wavelet transformation is only used for calculating recession constant. For further implication of wavelet analysisfurther work is required. The groundwater level change during recession is related to groundwater recharge. The recession constant and groundwater recharge can also be calculated with specific yield and groundwater level. So, the results from specific yield are used for comparison. The water balance parameters are computed by unsaturated moisture movement model. The unsaturated moisture model includes catchments parameters related to the runoff process.The water balance components obtained from water balance models arealmost accurate and are used in various land use practices and effective soil-water conservation. The water balance model provides parameters for the purpose of rainfall designs, storage yield, and prediction of meteorological, study of hydrological and ecological processes. The statistical comparison of groundwater recharge method and groundwater recharge from unsaturated water balance model shows master recession analysis method is the efficient method hydrograph recession analysis. It has illustrative test results as well as recession constant close to theoretical value.
Hydrograph recession also correlates climatic and geomorphologic features of the catchment. Hydrograph recession contents embedded information about the flow regime and hydro geological characteristic of the catchment. Hydrograph recession analysis should be carried in fast and objective manner. The different recession analysis method used in this study gives recession constants and groundwater recharge for the catchments. Therecession constants denote the slope of depletion curve. It also represents the rate by which water flow from the catchment to the runoff point. The flow in the catchment is also influenced by catchment slope and climate. The climatic information in hydrograph is further clarified by unsaturated moisture movement model. In unsaturated moisture model, soil moisture content in various soil layers are calculated at certain time period. It also contains the direction of flow at certain time. The amount and direction of flow is influenced by climatic condition and hydraulic conductivity of the catchment.The recharge component obtained from unsaturated moisture model is used to comparecharge calculated from different methods.
The recession constants calculated from various methods differs from each other. The recession constant depends on the selection of recession curve and procedure of its analysis. The calculation in this study also shows different recession constant and groundwater recharge values. To identify the best method, statistical tests are carried out. The wavelet transformation is a recent method applied for qualitative analysis of data which gives recession constant close to theoretical values. The study provides adequate information about various methods of hydrograph recession analysis and specific yield by which recession constant and groundwater recharge are calculated.
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9 APPENDICES
Appendix1. Calculation tables for recharge volume change for Marjasuo andRöyvänsuo catchments from individual recession curve analysis.
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Table3: Marjasuo catchment calculation table for individual recession curve for year 2012
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Table4: Marjasuo catchment calculation table for individual recession curve for year 2013
Table5: Röyvänsuocatchment calculation table for individual recession curve for year 2010
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Table6: Röyvänsuocatchment calculation table for individual recession curve for year 2011
Table7: Röyvänsuocatchment calculation table for individual recession curve for year 2012
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Table 2: Marjasuo catchment calculation table for Master recession curve for year 2011
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Table3: Marjasuo catchment calculation table for Master recession curve for year 2012
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Table4: Marjasuo catchment calculation table for Master recession curve for year 2013
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Table5: Röyvänsuo catchment calculation table for Master recession curve for year 2010
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Table6: Röyvänsuo catchment calculation table for Master recession curve for year 2011
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Table7: Röyvänsuo catchment calculation table for Master recession curve for year 2012
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Table 8: Röyvänsuo catchment calculation table for Master recession curve for year 2013
Appendix 3: Calculation of average groundwater level and average recession constant using groundwater level and specific yield for Marjasuo and Röyvänsuo catchments.
Table1: Marjasuo catchemt verage groundwater level and average recession constant for year 2010
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Table 2: Röyvänsuo catchemt verage groundwater level and average recession constant for year 2010
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Appendix 4: Output fluxes and soil moisture from unsaturated moisture balance model.
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Table 2: Marjasuo catchment output soil moisture from class 1D-U3M for year 2010
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- Rajib Maharjan (Autor:in), 2014, Hydrograph Recession Analysis for Finnish Watersheds, München, GRIN Verlag, https://www.grin.com/document/280738
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