Review of Soil Moisture Calculation Method. 2. Conceptual Model of Soil Moisture Over a Shallow Water Table

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1 1 Review of Soil Moisture Calculation Method 1. Introduction In accordance with the Habitats Directive, the Environment Agency is required to carry out an appropriate assessment when considering applications for abstraction licence renewals which may have an adverse impact on Sites of Special Scientific Interest (SSSIs). For some sites, one part of this assessment is the estimation of soil moisture under various abstraction scenarios, and comparison with threshold values to ensure that abstraction from groundwater does not cause stress to vegetation on the SSSI. The estimation of soil moisture content at sites above a shallow groundwater table has used a soil water budget methodology, including calculations of capillary rise of groundwater from the water table to the root zone. This note provides a review of the method and calculations of soil moisture content at groundwater-fed sites used by the Environment Agency Anglian Region. Section 2 provides an overview description of the conceptual model of soil moisture supply at wetland sites. Section 3 includes a literature review of calculations of capillary rise from shallow groundwater, and compares the values used in work for the Agency with other values from the literature. Section 4 describes the details of the numerical calculations, demonstrating that the approach is suitably precautionary. Section 5 describes a comparison of modelled and measured shallow groundwater levels, and provides a sensitivity analysis of soil moisture calculations to variations in groundwater level. Finally, Section 6 provides a summary of the review. 2. Conceptual Model of Soil Moisture Over a Shallow Water Table 2.1 Introduction This section provides an overview description of the conceptual model which underpins the calculations of soil moisture content at groundwater-fed wetland sites. The model is based on the concept of a capillary fringe: the rise of groundwater from the saturated zone in soil micropores, creating a zone above the water table of fully or partially saturated soil. If the capillary fringe is of sufficient thickness it may reach the root zone of surface vegetation, providing an additional supply of moisture over and above that present in the root zone from infiltrating precipitation. This is an accepted conceptual model described in, for example, FAO (1985), Freeze and Cherry (1979) and Schwärzel et al (2006).

2 2 The remainder of this section describes the principles of the soil moisture calculations used to support Environment Agency assessments of the potential impacts of abstractions from groundwater. 2.2 Soil moisture budget calculations The aim of the soil moisture calculations is to estimate the water available to vegetation compared with demand (evapotranspiration), and hence determine whether there is the possibility of vegetative water stress occurring. The stress threshold is defined in terms of soil moisture content, and the calculation process therefore comprises a time series of budget calculations of water entering the soil from the surface (precipitation), water being removed from the root zone by evapotranspiration, and potentially also water entering the root zone from below by capillary rise from the water table, in order to estimate the remaining soil moisture. Time series of precipitation (rainfall) for the site are provided from quality-assured UK Met Office rainfall data provided by the Environment Agency, and gridded for use with regional groundwater models. Time series of potential evapotranspiration (PE) data are provided from the Met Office Surface Exchange Scheme (MOSES) model. The calculation of water supply from groundwater by capillary rise is a function of soil properties (principally the moisture content at various suction pressures) and the vertical distance between the water table and the bottom of the vegetative root zone. If the height of the capillary fringe above the water table is sufficient to reach the root zone, then it is assumed that groundwater is available to satisfy some or all evaporative demand which cannot be met by infiltrating rainfall. Any remaining unsatisfied evaporative demand is met from soil moisture, increasing the soil moisture deficit. The process of capillary rise is illustrated in Figure 2.1. Figure 2.1 Capillary Rise of Shallow Groundwater to the Root Zone Capillary rise Root zone Water table Saturated zone The basic calculation steps are illustrated in Box 2.1. The details of the calculation method are further described in Section 4.

3 3 Box 2.1 Calculation of Soil Moisture Content Step Comment Calculate unsatisfied evaporative demand (PE minus rainfall) If there is no unsatisfied demand then assume no capillary flux to the root zone. Recalculate soil moisture content. If there is unsatisfied demand then calculate capillary flux to root zone. Capillary flux is a function of soil moisture content and properties, demand and depth to the water table. Calculate soil moisture content including the effects of rainfall, PE and capillary flux. The calculation of capillary rise is based on work reported by Rijtema (1969), which includes tables of the calculated steady state capillary rise as a function of flow velocity (i.e. evaporative demand), suction and soil moisture content for a uniform profile of twenty standard soil types. Section 3 compares these calculations with other values described in the literature. The model of capillary flux increasing soil moisture content is a numerically stable system with negative feedback. The rate of capillary flux is a function, inter alia, of soil moisture content, with lower moisture content inducing greater capillary flux (for a given depth to the water table). Capillary flux acts to increase soil moisture content. There exists, therefore, an equilibrium soil moisture content which is consistent with the calculated induced capillary flux; a greater flux would increase soil moisture content and act to reduce calculated capillary flux while, conversely, a lower flux would decrease soil moisture content and act to increase capillary flux. The basis of the capillary flux calculations is by interpolation between the values calculated by Rijtema (1969) of capillary rise and soil moisture content, to find a consistent solution. 3. Literature review estimates of capillary rise 3.1 Introduction This section describes the findings of a literature survey of measurements and calculations of capillary rise from shallow groundwater and evapotranspiration rates of vegetation on peat soils over shallow groundwater. Collated data values are compared with those described by Rijtema (1969). The calculated height of capillary rise is a function of soil unsaturated hydraulic conductivity, which in turn is a function of soil moisture content. The remainder of this section discusses various formulations to estimate soil moisture content and hydraulic conductivity, and hence capillary rise.

4 4 3.2 Peat Soil Moisture Retention Curves This section compares the soil moisture function for peat soils presented by Rijtema with other values in the literature. Schwarzel et al (2006) published parameter values for the van Genuchten (1980) function for 4 layers of peat soil in Germany. The van Genuchten function provides estimates of soil moisture content as a function of suction, according to the expression given in Equation 1. (1) θ is soil moisture content, φ is suction pressure (cm of water), θ s is saturated water content, θ r residual water content (assumed equal to zero in this case) and α and n model parameters. The model parameters provided by Schwarzel et al for 4 peat layers are as shown in Table 3.1. Table 3.1 Van Genuchten Parameters for 4 Peat Layers (Schwarzel et al, 2006) Layer Depth (cm) θs [-] α (cm-1) n Layer 1: very humified peat Layer 2: very humified peat, compacted Layer 3: humified peat, compacted Layer 4: weakly humified, reed sedge peat > The resulting water retention curves for these 4 peat layers are compared with the corresponding figures presented by Rijtema (1969) for a peat soil in Figure 3.1. The moisture retention figures given by Rijtema (1969) lie within the range of values derived for peat soils by Schwarzel et al (2006), and therefore appear consistent.

5 5 Figure 3.1 Soil Moisture Retention Curves for Peat Soils 3.3 Calculation of Capillary Rise This section compares the tables of heights of capillary rise given by Rijtema (1969) with other values published in the literature. Direct comparison is not always straightforward because of differences in the properties of standard soil types which are used to illustrate the calculations. The aim is more to demonstrate a consistency of approach and similarity of results. Bloemen (1980) presents the results of a computer calculation of steady state capillary rise from the water table in a variety of soil profiles. Calculations are carried out for a number of soil types, and tabulated examples are given for a groundwater depth of 200cm for various uniform soil profiles, and for some example multi-layered soil profiles. Figure 3.2 shows calculated capillary rise (cm) calculated for two sand soil types for various values of suction (cm) and flux rate, as presented by both Rijtema and Bloemen. Figure 3.3 shows similar calculated results for light clay soil types and Figure 3.4 for heavy clay soil types. Note that the choice of depth to groundwater (200 cm) used in the example presented by Bloemen causes the calculations of capillary rise to be capped at 200 cm (i.e. the soil surface).

6 6 Figure 3.2 Comparison of Capillary Rise for Medium Fine Sand (Rijtema, Solid Lines) and Cover Sand (Bloemen, Dashed Lines), for Various Suctions (cm). Figure 3.3 Comparison of Capillary Rise for Light Clay (Rijtema, Solid Lines) and Light Sandy Clay (Bloemen, Dashed Lines) for Various Suctions (cm).

7 7 Figure 3.4 Comparison of Capillary Rise for Basin Clay (Rijtema, Solid Lines) and Pot Clay (Bloemen, Dashed Lines) for Various Suctions (cm). The shapes of the curves of capillary rise presented by each author are very similar. For smaller values of suction the results are very similar. For larger suction pressures, the capillary rise predicted by Rijtema for medium fine sand is rather greater than predicted by Bloemen for fine sand. The converse is true for Rijtema s calculations for basin clay compared with Bloemen s calculations for pot clay. This could easily be because of differences in the assumed properties of the soil types; they are not necessarily directly comparable. The curves of capillary rise for light clay (Rijtema) and light sandy clay (Bloemen) are very similar for all values of suction up to cm (apart from values of capillary rise in excess of 200 cm, for the reasons previously discussed). Brandyk and Wesseling (1985) present results of calculations of capillary rise in a uniform sand profile, based on four different formulations of soil hydraulic conductivity variation with moisture content. Table 3.2 and Figure 3.4 present the results of their calculations of the maximum height of capillary rise using each formulation, compared with the values given by Rijtema for various sandy soils at a suction of cm (i.e. permanent wilting point). The methods for calculating K(h) used by Brandyk and Wesseling are fully documented in their paper, but method (a) is described by Rijtema (1965) and is the method used in his 1969 report.

8 8 Table 3.2 Calculations of Maximum Capillary Rise (cm) by Brandyk and Wesseling (1985) and Rijtema (1969). Flux (cm/d) Brandyk & Wesseling Method (a) Brandyk & Wesseling Method (b) Brandyk & Wesseling Method (c) Brandyk & Wesseling Method (d) Rijtema: coarse sand Rijtema: medium coarse sand Rijtema: medium fine sand Figure 3.5 Calculations of Capillary Rise in Sand Soils by Brandyk and Wesseling (1985) (a d) and Rijtema (1969) Again, direct comparison of the calculated values is confounded by the imprecise definition of the soil properties pertaining to each set of calculations. However, it is clear that, for the coarse and medium coarse sandy soils shown in Table 3.2, the values calculated by Brandyk and Wesseling bracket those presented by Rijtema. In other words, given the uncertainty in definition of soil properties and calculation of hydraulic conductivity, there is reasonable agreement between the calculations.

9 9 4. Review of Numerical Calculations 4.1 Overview of Calculation Process The aim of the numerical calculations is to find equilibrium values of soil moisture content and height of capillary rise which are consistent with each other. If they cannot be solved analytically, then negative feedback systems such as this are usually solved iteratively through the use of an error function. The solver will take a guess at a solution for soil moisture content and calculate the resulting height of capillary rise and the soil moisture content consistent with that height of capillary rise. This first solution will be compared with the original guess, and an error function calculated which describes the difference between the two. A second guess will then be formulated as a function of the original guess and the error function. Calculations are repeated until the size of the error function falls below a specified tolerance (i.e. the numerical accuracy of the solution is considered acceptable). This iterative approach is not straightforward to implement in a spreadsheet using only Excel formulae. A pragmatic solution has therefore been developed which calculates a trial solution of soil moisture content for a variety of values of flux rate (i.e. unsatisfied evaporative demand), and then reverse calculates the flux rate consistent with that soil moisture content. Each solution is then tested for internal consistency (i.e. is the size of the error function acceptably small). The final calculated soil moisture content is that which is consistent with the assumed flux rate and antecedent soil moisture content (for the selected soil type). In reality, capillary rise is a continuous function of soil moisture content (and hence hydraulic conductivity) and flux rate. For the purpose of spreadsheet calculations, this continuous function has been described by a family of curves, each specific to a value of flux rate, relating capillary rise to soil moisture content. Each of these curves has then been divided into sections, separated by the fixed data points presented by Rijtema (1969). The spreadsheet calculations find a consistent solution for antecedent soil moisture content, flux rate and hence capillary rise, which results in a final value of soil moisture content which lies in the same section of the same curve as the initial value, and is therefore consistent to within the resolution of the values presented by Rijtema. The final solution for soil moisture content is then found by linear interpolation between the boundary values of that section of the appropriate curve. The table of values of capillary rise for peat soil presented by Rijtema (1969) is reproduced in Table 4.1. The resulting solution curves and sections for peat soil are shown in Figure 4.1.

10 Technical Note 10 Table 4.1 Calculated Capillary Rise (cm) for Peat Soil (Rijtema, 1969) Flux rate (cm/d) suction (cm) moisture content (%) AMEC Environment & Infrastructure UK Limited

11 11 Figure 4.1 Curves of Capillary Rise in Peat Soil Against Suction, for Various Values of Fflux Rate (cm/d) (Rijtema, 1969) 4.2 Definition of Field Capacity and Wilting Point For the purposes of these calculations, soil field capacity and wilting point are defined as being the moisture contents at 100 mb and mb suction, respectively (equivalent to 100 cm and cm suction). The accepted working definition of wilting point is at a slightly different suction of mb (15 bar). Definitions of field capacity in the literature vary, but the accepted working definition is the moisture content at a suction of 0.33 bar (330 mb). By linear interpolation between the tabulated values, soil moisture contents for peat soils at 0.33 bar and 15 bar have been calculated as shown in Table 4.2.

12 12 Table 4.2 Soil Moisture Content at Various Suction Pressures for Peat Soil Suction (mb) Water Content(%) Comment Full saturation Field capacity (soil moisture spreadsheet) Field capacity (accepted definition) Wilting point (accepted definition) Wilting point (soil moisture spreadsheet) The difference therefore in the calculated soil moisture content at wilting point is negligible (0.4%). The difference in calculated soil moisture content at field capacity is larger (7.7%). This affects the calculation of the stress threshold against which the calculated soil moisture content is compared in order to determine the risk of vegetative stress occurring. The stress threshold is calculated as the average of the calculated moisture contents at wilting point and field capacity. In the soil moisture spreadsheet, the stress threshold is calculated as 51.4% (the average of 76.3% and 26.5%). By the accepted definitions, the stress threshold would be 47.8% (the average of 68.6% and 26.9%; 4.4% lower than the spreadsheet value). The values used therefore represent a worst case estimate of likely vegetation stress. 4.3 Root Depth Calculations typically assume a value for rooting depth of 250 mm or 25 cm (although this can be varied). There is tremendous variability in root depth between types of grass, and for water balance calculations it is probably appropriate to consider the depth to which the deeper feeder roots penetrate.

13 13 Wessoleck et al (2011) carried out simulations of capillary rise and actual evapotranspiration from grassland sites using rooting depths in the range 40 cm 100 cm, depending on soil type. Bloemen (1980) assumed root depths in the range 19 cm 45 cm for calculations of capillary rise in a number of soil profiles. In this context, the values used here of 25 cm could be considered to be below average for grass species. Increasing the assumed root depth will reduce predicted stress on vegetation, and so the use of a low (in this case 25 cm) value represents a worst case estimate. 5. Measurements of Shallow Groundwater Levels 5.1 Introduction Calculations of soil moisture content carried out using the method described in Section 4 require as input a time series of water level data at the assessment site. These data are routinely provided by the Environment Agency s North East Anglian Chalk (NEAC) regional groundwater model, which is calibrated against observations from dip wells and gauge boards to provide accurate predictions of groundwater levels expressed as metres above Ordnance Datum (maod). Knowing the surface elevation at the assessment site (as maod), the depth to groundwater from the ground surface may be calculated. In the past data would have been provided by predecessor models, for example the Yare and North Norfolk (YNN) model. This section compares model predictions of water level at four sites adjacent to Catfield Fen which is part of the Ant Broads and Marshes SSSI, with measured water levels from dip wells and gauge boards, and examines the sensitivity of the soil moisture calculations to small differences in input water level data between measurements and model predictions. It is demonstrated that the use of water level values taken from the NEAC model (as opposed to measurements) does not materially affect predictions of soil moisture, and hence the integrity of conclusions based on them. By implication, it is therefore appropriate to use model predictions of water levels for assessment of sites for which observations of shallow groundwater levels are not available. 5.2 Hydrological Monitoring Sites Comparisons of measured and modelled water levels have been carried out for four monitoring sites near Catfield Fen. The locations of the monitoring sites are as shown in Figure 5.1. Table 5.1 shows the corresponding NEAC model cell coordinates for each site.

14 14 Table 5.1 Hydrological Monitoring Sites and NEAC Model Cell Coordinates for Which Water Levels Have Been Compared Site Reference NEAC Model Cell (Row Column) TG32/605a (dip well) TG32/617b (dip well) TG31/790a (dip well) TG32/711 (gauge board)

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16 Water level (maod) Water level (maod) 16 Figure 5.2 Measured and Predicted Water Levels, TG32/605a /12/ /12/ /12/ /12/ /12/ /12/2013 6nea537 R136C518 TG32/605a Figure 5.3 Measured and Predicted Water Levels, TG32/617b /12/ /12/ /12/ /12/ /12/ /12/ nea537 R135C519 TG32/617b

17 Water level (maod) Water level (maod) 17 Figure 5.4 Measured and Predicted Water Levels, TG31/790a /12/ /12/ /12/ /12/ /12/ /12/ nea537 R141C521 TG31/790a Figure 5.5 Measured and Predicted Water Levels, TG32/ /12/ /12/ /12/ /12/ /12/ /12/ nea537 R135C521 TG32/711 In general there is good agreement between modelled and measured water levels at 3 of the 4 sites (TG32/605a, TG32/617b and TG31/790a). The seasonal variation in groundwater levels is well captured, and annual minimum water levels (the features of most interest since they will correspond with periods of minimum soil moisture content) are accurately represented.

18 18 At site TG32/711 the model generally captures the seasonal variation in water levels, but consistently under-predicts compared with measured water levels at the gauge board. Minimum water levels are under-predicted by between 10 and 25 cm; maximum water levels by slightly less. 5.4 Comparison of Soil Moisture Predictions Soil moisture calculations were carried out using the method described in Section 4, for each of the monitoring sites. In each case, two sets of calculations were performed using measured and modelled water levels, respectively. In each case, time series of rainfall and potential evapotranspiration (PE) were taken from the relevant model cell of the NEAC 4R (recharge) model. Rainfall and PE data are therefore identical for each pair of calculations but vary between monitoring sites. Calculations of soil moisture content are time-stepping; that is, the soil moisture content on each day is calculated as a change from the previous day s value. The assumed soil moisture content at the beginning of the calculation period is therefore important, and use of an inaccurate initial value can affect the results for the first year of the calculation period. This is known as model spin-up. Calculations based on modelled water levels, for which daily values are available throughout the model period, normally commence on January 1 st and it is assumed that on this day the soil is at field capacity. This is a reasonable assumption (providing calculations do not commence in an abnormally dry year), and to avoid any spin-up effects calculations normally commence a few years prior to the period of interest, with the calculations for the first year being discarded. Measurements of water levels span a shorter time period, may not commence in winter when the soil is at field capacity and may contain gaps due to, for example, temporary equipment malfunction. As such, soil moisture calculations based on measured water levels are subject to spin-up in the first summer of the calculation period, as will be evident. Predictions for the first summer prior to the soil returning to field capacity should therefore be disregarded. Figures 5.6 to 5.9 compare measured and modelled water levels (upper panel) and predictions of soil moisture content (lower panel) for each of the four sites, for the period 01/01/2006 to 21/11/2011, although measurements of water levels at each site are only available for a subset of this period. Differences in predicted soil moisture content based on measured and modelled water levels are evident in the first summer of the simulation period due to spin-up (as discussed above). This is a function of data availability rather than the modelling methodology. Predictions of soil moisture content in the summers of 2007 and 2008 agree very well, with differences generally of order 2 3%. Differences in predicted soil moisture content are slightly greater at site TG32/711 due to the larger differences between modelled and measured water levels at that site. Soil moisture predictions based on modelled water levels are lower than those based on measured water levels, Larger differences in predicted soil moisture content are evident in summer 2009 at sites TG32/617b, TG31/790a and TG32/711. In all three cases, predicted soil moisture content based on modelled water levels is lower than that based on measured water levels, and the use of modelled water levels is therefore precautionary in these instances.

19 moisture content (%) modelled water level (cm below assumed base of Root Zone) Technical Note 19 Figure 5.6 Modelled and Measured Water Levels and Soil Moisture Content: TG32/605a Groundwater levels and Soil Moisture Content: scenario comparison /12/04 31/12/05 31/12/06 31/12/07 31/12/08 31/12/09 31/12/ water level: R136C518 Historic run 6nea537 water level: TG32/605a /12/04 31/12/05 31/12/06 31/12/07 31/12/08 31/12/09 31/12/10 moisture content (%age) R136C518 Historic run 6nea537 moisture content (%age) TG32/605a Stress threshold Field capacity Ooziness threshold

20 moisture content (%) modelled water level (cm below assumed base of Root Zone) Technical Note 20 Figure 5.7 Modelled and Measured Water Levels and Soil Moisture Content: TG32/617b Groundwater levels and Soil Moisture Content: scenario comparison /12/04 31/12/05 31/12/06 31/12/07 31/12/08 31/12/09 31/12/10 0 water level: R135C519 Historic run 6nea537 water level: TG32/617b /12/04 31/12/05 31/12/06 31/12/07 31/12/08 31/12/09 31/12/10 moisture content (%age) R135C519 Historic run 6nea537 moisture content (%age) TG32/617b Stress threshold Field capacity Ooziness threshold

21 moisture content (%) modelled water level (cm below assumed base of Root Zone) Technical Note 21 Figure 5.8 Modelled and Measured Water Levels and Soil Moisture Content: TG32/790a Groundwater levels and Soil Moisture Content: scenario comparison /12/04 31/12/05 31/12/06 31/12/07 31/12/08 31/12/09 31/12/10 0 water level: R141C521 Historic run 6nea537 water level: TG31/790a /12/04 31/12/05 31/12/06 31/12/07 31/12/08 31/12/09 31/12/10 moisture content (%age) R141C521 Historic run 6nea537 moisture content (%age) TG31/790a Stress threshold Field capacity Ooziness threshold

22 moisture content (%) modelled water level (cm below assumed base of Root Zone) Technical Note 22 Figure 5.9 Modelled and Measured Water Levels and Soil Moisture Content: TG32/711 Groundwater levels and Soil Moisture Content: scenario comparison /12/04 31/12/ water level: R135C521 Historic run 6nea537 water level: TG32/ /12/04 31/12/09 moisture content (%age) R135C521 Historic run 6nea537 moisture content (%age) TG32/711 Stress threshold Field capacity Ooziness threshold

23 Technical Note Summary and Conclusions 6.1 Review of Conceptual Model The method of calculation of soil moisture content is based on the concept of capillary rise of groundwater from the water table. If the height of the capillary fringe above the water table is sufficient to reach the root zone, some or all evaporative demand may be met from groundwater; The height of the capillary fringe is a function of evaporative demand (flux rate) and soil properties; This conceptual model is accepted and widely described in the literature. 6.2 Review of Numerical Model and Parameter Values The adopted definition of field capacity (soil moisture content at 100 mb suction) results in a slightly higher parameter value than the commonly used definition of moisture content at 330 mb suction; The value of rooting depth used in the calculations (250 mm) is lower than many values reported in the literature; These choices of parameter values result in precautionary (i.e. lower) estimates of soil moisture content than would result from using literature values; The tables of capillary rise, as a function of flux rate and soil water retention curve, derived by Rijtema (1969) are consistent with other values in the literature. 6.3 Comparison of Calculations with Measured and Modelled Water Levels Predictions of water levels from the NEAC regional groundwater model have been compared with measured values from three dip wells and one gauge board in East Anglia, at sites in the vicinity of Catfield Fen; Soil moisture calculations have been carried out using both sets of water level data, and the results compared; There is generally good agreement between modelled water levels and measurements from dip wells; Agreement is less good between modelled water levels and those from one gauge board site; As expected, the resulting predictions of soil moisture content agree well when the modelled and measured water levels agree well but there is less good agreement when differences between modelled and measured water levels are greater;

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