Theory of the generalized chloride mass balance method for recharge estimation in groundwater basins characterised by point and di ff use recharge

Introduction Conclusions References


General:
The response from the authors to my first round of review comments was verbose and did not address the basic issues of the manuscript.Hence, I provide here additional comments, given that most of the previous ones were refuted or not properly dealt with.In the interests of providing clarity for readers and the authors, only the most fundamental errors in the manuscript are identified, with a scope to writing in the clearest possible manner: Author Reply: We thank the Referee 1 for providing additional technical comments.By this way, we may be able to provide further clarification, and revise the manuscript where it is needed.
Referee 1_C1.The background literature on the topic of the paper is misrepresented.It is not the case that previous authors discount saturated zone CMB where preferential flow occurs.Only the authors' prior discredited HESSD manuscript attempts this.It is the unsaturated zone CMB that does not apply where unsaturated zone preferential flow occurs.The authors use one method to undermine a different one.
Author Reply: We consider this is an oversight.We thank the Referee 1 for raising this issue so that we can provide further clarification.
We agree that previous authors such as Wood et al (1997) stated that the unsaturated zone CMB does not apply where preferential flow or point recharge occurs.Apart from Somaratne et al (2013) and this manuscript, to the best of our knowledge, no other papers have considered the validity of saturated zone CMB to groundwater basins where point recharge occurs.We highlighted two problems (1) boundary conditions of the conventional CMB are not applicable when point recharge occurs (2) Representative groundwater chloride samples cannot be obtained when point recharge occurs due to mixing.These aspects were thoroughly discussed in detail to our Author Reply to Prof. Warren Wood and are not repeated here.
Please read the document entitled "Why the Conventional CMB Fails in Karst".

Referee 1_C2:
The investigation assumes that there is no mixing in either the unsaturated zone or the saturated zone, between preferential flow and diffuse flow.This assumption must be acknowledged.Regardless, it is entirely indefensible to consider this a valid assumption for all systems with preferential flow, because despite unsaturated zone preferential flow, there may be saturated zone mixing of waters originating from diffuse and bypass flows.The no-mixing assumption is most certainly not applicable to Uley South (calcrete capping underlain by sand).The relatively small variations in Cl from dozens of sample sites across this aquifer are testament to that.
Author Reply: Thank you for comments.We highlight the assumption that 'no mixing occurs in either the unsaturated zone or at the watertable plane'.If there is mixing in the unsaturated zone prior to reaching the watertable plane or mixing at the watertable plane there is no need for a bi-model approach as derived in this paper or bi-model presented in Wood et al (1997).Below is an extract from our reply to Prof. Warren Wood: "Of course, there is an area of uncertainty if the two streams (point recharge and diffuse recharge) mix well before arriving at the watertable, OR mix well in the watertable.If this happens no distinguishable point or diffuse recharge crosses the watertable plane.Therefore, the recharge flux arriving at the watertable plane may have the chloride concentration as in saturated zone (at least approximately) and the conventional CMB is still applicable.This may apply to the case of point recharge through root channels, burrows, cracks and minor fissures or in large regional aquifers, such as the case reported by Herczeg et al (2003) where point recharge is 10% of the total recharge in the regional Tatiara catchment (>500 km 2 )." The mixing is considered in the saturated zone and that is why groundwater chloride c g is expressed within the range: c s ≤ c g ≤ c gd..
With regards to the comment on 'calcrete underlain by sand', this is an assumption based on an erroneous conceptual model.Calcrete is limestone formed by the cementation of soil, sand, gravel and shells, by calcium carbonate deposited primarily by evaporation.Apart from the recent coastal monitoring well drilling programmes, all historical investigation/monitoring/production wells have been drilled by the percussion drilling technique.As a result of this drilling process, some of the wells' returned drill cuttings may look like 'unconsolidated sand' due to pulverisation of the calcrete (of cemented sand).Drillers logged these wells as 'sand', but they are carbonaceous sand and subject to dissolution and therefore in general, highly porous flow paths or cavities exist Referee 1_C3: Equation 10 is in direct contradiction to the conceptual model.Equation 10's Cg is clearly the mixed groundwater Cl concentration, whereas Figure 5 (and much of the case study descriptions) refer to distinct and separate high Cl-low Cl water bodies ("bubbles") that somehow defy dispersion processes.Which case is it -mixing or no mixing in the groundwater?
Author Reply: This is best understood as a gradation between the two extremes of all diffuse to all point recharge.As such there will be a gradation of mixing between these two extremes.As Referee 1 stated, we agree that Cg is the mixed groundwater.The conceptual model is a general presentation and as such not specific to any case studies.For example, see Figure 4, where Cs is directly recharging the groundwater and mixing with ambient groundwater chloride.We have used the words 'fresh water pockets', 'bubbles' and 'plumes' to describe the wide spectrum of chloride values possible between the two end members; that is chloride associated with point recharge and ambient groundwater in the plume.The dispersion process is not ignored.Referee 1_C4: Eq 10 is wrong.A "flow across the watertable" would need inflows of RuCu + QpCs, and groundwater outflows of (Ru+Qp)Cg.This is not withstanding the lack of lateral groundwater flows here, which is equally problematic for the analysis.There is simply no way that the different water inflows at a point are somehow able to remain isolated as they discharge below the watertable.
Author Reply: The Equation 10 is correct.Firstly please refer to Page 317, Line 21 to Page 318, Line 5. It states: "This implies that groundwater chloride in the saturated zone is derived only from recharge and that there is no chloride loss from the saturated zone through evapotranspiration.It is also assumed that lateral fluxes, and upward and downward leakages do not result in changes in chloride concentration, and there is no irrigation water recycling or waste water irrigation.Using the above assumptions, groundwater chloride in the saturated zone is determined only by the diffuse and point recharge fluxes crossing the watertable." Now consider two streams of chloride arriving at the watertable plane.The chloride mass arriving at the watertable plane as a result of diffuse recharge R u is ( .Similarly, chloride mass flux arriving at the watertable plane as a result of point recharge (Q p ) is .Therefore, total chloride mass about to cross the watertable plane is ( . Unless two streams mix at the watertable plane, Ru and Qp crosses the watertable plane with their respective chloride concentration.At the watertable plane (where saturated zone starts), there is no need to use C u , (which is chloride concentration just above the watertable plane) any more as it has been defined as the C gd (which is basically C u in the watertable plane).In between, there is no mixing and no chloride loss or gain.Therefore, on reaching the watertable plane unmixed, both point and diffuse recharge fluxes cross the watertable plane still unmixed with total chloride mass of .No mixing at the watertable plane is an important assumption and we have highlighted this in the revised manuscript.
The mixing occurs in the saturated zone below the watertable, after penetrating the watertable, driven by lateral flow and solution equilibrium.We agree that different water flows do not remain isolated but rather that mixing occurs giving the broad spectrum of chloride between the two end members.This we have indicated in page 318, line 7 as: c s ≤ c g ≤ c gd. .Referee 1 suggests that groundwater outflows can be expressed by (R u + Q p ) c g. after crossing the watertable plane.To write the above expression, both point recharge and diffuse recharge need to mix at the watertable plane.The above concept, (R u + Q p ) c g , is the fundamental basis of the conventional CMB.
We provide the relevant section from Author Reply to Prof. Wood below: "Of course, there is an area of uncertainty if the two streams (point recharge and diffuse recharge) mix well before arriving at the watertable, OR mix well in the watertable.If this happens no distinguishable point or diffuse recharge crosses the watertable plane.Therefore, the recharge flux arriving at the watertable plane may have the chloride concentration as in saturated zone (at least approximately) and the conventional CMB is still applicable.This may apply to the case of point recharge through root channels, burrows, cracks and minor fissures or in large regional aquifers, such as the case reported by Herczeg et al (2003) where point recharge is 10% of the total recharge in the regional Tatiara catchment (>500 km 2 )."

Referee 1-C5:
There is considerable confusion expressed by the authors regarding equation 10.For example, "initial" and "at the end of delta-t" don't apply to a steady-state analysis.They are trying to do a mass balance across a plane (the watertable), and hence the LHS derivative term has no meaning, because a plane has no volume.That is, Cgd = Cu, and the RHS is obviously zero, which one would expect.The inference from equation 10 is that diffuse and point recharge crossing the watertable are somehow able to remain immiscible, and remain in the aquifer with their unsaturated zone concentrations.This is entirely non-physical.
Author Reply: Thank you for the comment.Initial and at the end of delta t was removed from the text.First part of the comments addressed after Referee 1's first round of comments.We do not attempt to obtain mass balance across a plane but rather in the groundwater storage.Any changes to groundwater chloride in the storage occurs only through recharge fluxes crossing the watertable plane.That is why in Equation 10 chloride mass balance was taken as the difference between just before arriving watertable plane and at the watertable plane.As mentioned before, fundamental assumption is the no mixing occurs (between diffuse and point recharge) in the unsaturated zone or at the watertable plane.Apart from chloride associated with recharge fluxes, nothing else can change the chloride mass in storage (What we have stated in the manuscript is: "groundwater chloride in the saturated zone is determined only by the diffuse and point recharge fluxes crossing the watertable).
Referee 1-C6: Regardless of point 5. above, equation 10 is not needed to continue through the authors' mathematics.Equation 11 is simply PCp+D = RuCgd + QpCs (Equation R1) and does not require Eq. 10 as suggested.Hence, despite what the authors say, there is no groundwater mass balance included in their investigation.It is misleading to suggest this.To obtain Eq. 11, they simply drop the Qo term from eq. 9.
Author Reply: This is the authors' earliest approach and a short cut.Equation ( 9 Referee 1-C7: Following from this, equation R1 above is rearranged to Ru=(PCp+D -QpCs)/Cgd (Equation R2), which requires that the Cgd or Cu (which are the same) be knowni.e. that the Cl in the unsaturated zone immediately above the watertable is characterised.Hence, the once-simply and elegant saturated-zone CMB method now requires un-saturated zone measurements, not to mention some estimate of Qp (point recharge).Equation 13c is then simply the RHS of equation R2 plus Qp.
Author Reply: We highly appreciate Referee 1's great interest and enthusiasm with respect the Equations and CMB method.The very advantage of having C u or C gd in the equation with Q p is explained below, taking relevant sections from our reply to Prof. Wood.
As mentioned in the Somaratne et al ( 2013) manuscript (Hydrological functions of sinkholes...), one of the main disadvantage of applying conventional CMB to point recharge dominant groundwater basins is the difficulty of getting representative groundwater chloride.
1.When groundwater compartment (mixing) occurs, it is not possible to obtain representative samples due to a wide spectrum of chloride values that are possible between two end members; that is chloride associated with point recharge and ambient groundwater in the plume.This is similar to Aquifer Storage and Recovery (ASR) wells, where different concentrations of groundwater chloride exist, radiating from the point of recharge location outwards to ambient groundwater chloride concentrations.This is true no matter how small or large the volume of point recharge is.For example in Fig. 4 (see page 331), groundwater chloride for a drainage well (which is point recharge source) is (21.1 ± 21.6 mg/L) and for a monitoring well, (which is a sampling point) is (63 ±26 mg/L).In the Poocher Swamp fresh water lens, the surface water chloride concentration is 28 mg/L in the Swamp, 40 mg/L in nearby wells, and outside the lens in the diffuse recharge zone the chloride concentration is greater than 550 mg/L.When such extreme variation in groundwater chloride occurs due to extreme point recharge, the very definition of 'representative samples' becomes questionable.Even if one increased the sampling density, in the hope of getting average chloride values, it could still grossly underestimate the recharge.
2. In real world situations, when the aquifer is not fully mixed there are difficulties in obtaining average representative chloride samples from heterogeneous (karstic aquifers).We have shown in an earlier manuscript, doi:10.5194/hessd-10-11423-2013(Hydrological functions of sinkholes..), that it is not possible to measure representative samples due to the unknown extent of both the plume and the spread of conduits.We have shown using salinity profiles that low salinity freshly recharged water from point sources move at varying depths in the Blue Lake capture zone, Mount Gambier.We have cited an example from Herczeg et al (1997)  3.An attractive feature of the generalized CMB equation is that it is not necessary measure groundwater chloride (c g or Cl gw in Wood, 1999) as it is not required in the equation.Instead generalized CMB uses only c gd (OR C uz in Wood, 1999) which can be obtained from soil water extraction described above or measuring diffuse zone chloride concentrations.Therefore, uncertainty associated with extreme variability of groundwater chloride concentrations due to extreme point recharge is not affected on calculated recharge (see page 319, Eq. 13c).
Please read the document entitled "Why the Conventional CMB Fails in Karst".
Referee 1-C8: The approximation to produce eq.13d from eq. 13c is both unnecessary and has important implications.It assumes that all the Cl load to the aquifer occurs via diffuse flow, despite preferential flow occurring.That is, it is eliminating the QpCs term from the mass balance RuCgd = PCp+D -QpCs.Note that, despite what is suggested by the authors, eq.13d and eq. 3 are not the same, because firstly eq. 3 is a water balance and eq.13d is a salt balance, but also one would assume that an extension to eq. 3 would involve properly diverting salt into its constituent pathways.Dropping QpCs from the mass balance will have only small implications in some cases only.
) contains C u and the Equation 11 contains C gd .The relation of c u =c gd from Equation 10 is necessary to highlight all the related assumptions, particularly No Mixing of Two Streams (point and diffuse recharge) at the Watertable plane.With respect to dropping Q o , it is stated that: "for closed basins where Q o =0." (see page 318 Line 14).
in their study on Poocher Swamp sinkhole recharge.Herczeg et al (1997) established three monitoring wells at 10 m, 50 m and 150 m down-gradient of the two sinkholes to study the water level behaviour during recharge.The first two (shallow) wells terminated at 6 m below water level, and the third well (at 150 m) terminated at 50 m depth and about 35 m below the water level.The maximum water level rise was observed at the well 150 m from the sinkhole indicating a direct sub-surface connectivity to the sinkhole.