SEARCH

SEARCH BY CITATION

Keywords:

  • subsidence;
  • inversion;
  • water management

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Method
  6. 4. Results
  7. 5. Conclusions
  8. References

[1] The surface movement in the Krimpenerwaard polder in The Netherlands results from primary or hydrodynamic settlement/swelling, secondary or creep settlement/swelling, and peat oxidation. We used surface movement measurements in a Bayesian inversion scheme to disentangle the contribution of these three processes to the subsidence. The prior information, including spatial correlations, appeared to be crucial in our procedure. This prior information was derived from geological modeling incorporating the most important uncertainties. The inversion procedure allowed us to quantify the contributions of the three processes with unprecedented accuracy. Surface rise in the data was related to swelling of the clay layers, even though swelling was considered infeasible in the prior information. Despite this, the irreversible nature of peat oxidation was preserved. The improved subsurface description offers prospects for identification of incorrect information and for better assessments of the effects of water management.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Method
  6. 4. Results
  7. 5. Conclusions
  8. References

[2] The long tradition in the Netherlands of draining marshland for agriculture by creating polders has caused the land surface in some areas to subside by as much as several meters. Ongoing and future drainage will bring about further subsidence. As the subsidence is irreversible, long-term water management must take account of predicted subsidence. It is also essential to assess the consequences of predicted subsidence on the hydrological system, nature and the safety of buildings and infrastructure.

[3] The manipulation of the water level in the polders causes surface movement through the settling or swelling of the overburden and the oxidation of peat in the unsaturated zone. Disentangling the magnitude of these contributions appreciably improves the validation of groundwater flow models, and the reliability of the predicted impact of water management decisions.

[4] In this paper, we apply a Bayesian inversion method to subsidence data from the Krimpenerwaard polder in the west of The Netherlands, in order to unravel the contributions of primary and secondary settlement or swelling and peat oxidation. The polder (Figure 1) is a single hydrological unit bounded by the Lek and Hollandse IJssel rivers and the Vlist stream.

image

Figure 1. Aerial view of the Krimpenerwaard polder.

Download figure to PowerPoint

2. Data

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Method
  6. 4. Results
  7. 5. Conclusions
  8. References

[5] The surface movement observations used in the procedure were acquired through leveling campaigns in the south–east of the Krimpenerwaard in 1984 and 2000 (Figure 2a). These observations indicate that parts of the polder have experienced a rise of up to 8 cm, though the predominant trend is around 10 cm of subsidence. The precision of the data depends on measurement accuracy (2 cm), seasonal variations (2–2.5 cm), daily variations (3.5 mm), local terrain variations (up to 20 cm), and reference uncertainties (1–2 cm). Assuming a normal distribution with a 90% confidence level, a standard deviation of 5.1 cm was derived. Since the reference benchmarks used in the two leveling campaigns do not match perfectly, the standard deviation was scaled using the distance between corresponding leveling stations; this yielded a laterally varying data uncertainty.

image

Figure 2. (a) Observed surface movement between 1984 and 2000 derived from surface level height measurements in the Krimpenerwaard polder. Note that both subsidence (negative surface movement) and uplift (positive surface movement) are observed. (b) Surface movement computed from the inverted estimates of the primary settlement, creep settlement, and peat oxidation. (c) Surface movement computed from the prior estimates of the primary settlement, creep settlement, and peat oxidation. Note that from the prior estimates no uplift is computed.

Download figure to PowerPoint

3. Method

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Method
  6. 4. Results
  7. 5. Conclusions
  8. References

[6] The practice of adjusting the water level in polders, coupled with seasonal variations, cause the unconsolidated upper layers of the ground to settle or to swell and the peat in the zone above the water table to oxidize. The result is surface movement. Two types of settlement can be distinguished: primary or hydrodynamic settlement and secondary or creep settlement. To express the relation between the surface movement and the settlement or swelling of the overburden we follow Koppejan [1948]. The settlement due to the oxidation of peat depends exponentially on the oxidation rate: δhox = h(1 − equation image), where δhox is the reduction in the thickness of the peat layer due to oxidation, h is the unsaturated thickness of the peat layer, vox is the peat oxidation rate, and δt is the oxidation process time.

[7] We parameterized the subsurface of the Krimpenerwaard on a regular grid. Each grid cell was assigned specific soil properties corresponding to one of the 10 soil types we distinguished. Our forward equations contained 6 parameters for each soil type, except for the peat layer, which contained 7 parameters. The prior model took account of the uncertainties in these 61 soil parameters (10 soil types, 6 parameters for each layer and the peat oxidation rate). A sensitivity analysis identified the peat oxidation rate to be most influential. Therefore, a full Monte Carlo analysis of the uncertainties of these parameters was performed [see Muntendam-Bos et al., 2008; Muntendam-Bos and Fokker, 2008]. The uncertainties of the remaining 60 parameters were mapped with a Latin Hypercube method [Iman and Conover, 1982]. In the Koppejan [1948] relations, whether settlement or swelling occurs is related to a lowering or rise in the water table, respectively, and not to the uncertain soil parameters (The reloading parameters were used to calculate swelling). In the modeling we used water table data from the local water boards. During the period investigated, all these data were drops in the water table.

[8] For a set of surface movement data our parameterization yields a linear, coupled system of equations, represented by Gm = d, where G is the coefficient matrix relating the data (d) to the model parameters (m). The formal least-squares solution of our system is [see Tarantola, 2005; Muntendam-Bos et al., 2008] m = m0 + (CmGTGCmGT + Cd)−1(dGm0), where m0 is the prior model, and Cd and Cm denote the data and prior model covariance matrices, respectively. The model parameterization allows us to distinguish between primary settlement, secondary settlement, and peat oxidation in the observed surface movement. The solution of the system thus yields estimates of the contribution of each of these three processes to the overall change in surface level.

[9] The result of the inversion is dependent on the prior information: the prior model (m0) and the prior model covariance matrix (Cm). The non-zero covariance in Cm quantifies the expected relationships between points [Muntendam-Bos et al., 2008]. Such knowledge is often available, even when the absolute values of the initial compaction models are uncertain.

4. Results

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Method
  6. 4. Results
  7. 5. Conclusions
  8. References

[10] Figures 2b and 2c present the total subsidence as calculated with the prior model and with the inverted result. The agreement of the inverted result with the measurements (Figure 2a) is excellent; even the apparent swelling in certain areas is reproduced.

[11] Figure 3 shows the three shallow surface movement processes for both the prior model and the inverted model estimate. The prior model does not exhibit swelling, but the inverted model does, with contributions of up to 5 cm and up to 10 cm in the primary settlement and creep settlement, respectively. Note that in the prior model these areas exhibit the largest compaction for both processes.

image

Figure 3. The (a) primary settlement, (b) creep settlement, and (c) peat oxidation of the prior model compared to the (d) primary settlement, (e) creep settlement, and (f) peat oxidation of the inverted model. Note the swelling in both the primary and creep settlement of the inverted model, while at the same time the inversion honors the fact that peat oxidation is irreversible.

Download figure to PowerPoint

[12] The swelling derived in the inferred model cannot be related to the uncertainties in the prior model. In other words, the range of uncertainties in the soil parameters leads to subsidence. In the Koppejan [1948] relations between surface motion and underlying processes, swelling can result from a reduction in effective stresses (e.g. due to a rise in groundwater levels). Thus the water level in these areas must have risen in the period investigated. In the areas exhibiting swelling the subsurface comprises a thick layer of heavy clays (Echteld Formation) fully bound by channels of coarse sand and overlain by a thin layer of peat (Holland peat). This suggests either that - contrary to the data supplied by the water board - the water level in this area has risen, or that there is an error in the reference point used in the leveling campaign: if the reference point subsides relative to the predominantly clayey area, the area will appear to exhibit net swelling.

[13] Despite the fact that inverse modeling suffers from non-uniqueness and ill-conditioning and that the model outcome is not constrained to negative numbers, the method honors the irreversibility of peat oxidation (Figure 3f). The pattern of the oxidation is the same for both models. However, the degree of peat oxidation is markedly smaller in the inverted model estimate than assumed in the prior model (Figure 3c).

[14] The error estimates of the inverted model can be derived from the diagonal elements of the posterior covariance matrix (Figure 4). For the peat oxidation and creep settlement, these errors are two orders of magnitude smaller than the model values. For the hydrodynamic compaction, the error is one order of magnitude smaller than the model values. The largest errors coincide with the areas experiencing the most significant adaptation of the prior model towards the model estimate.

image

Figure 4. Error estimates derived from the diagonal elements of the posterior covariance matrix for the (a) primary settlement, (b) creep settlement, and (c) peat oxidation.

Download figure to PowerPoint

5. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Method
  6. 4. Results
  7. 5. Conclusions
  8. References

[15] In this paper, three shallow processes inducing subsidence have been successfully disentangled, using a method incorporating prior information on geological correlations. Though the prior information does not consider the possibility of swelling, the uplift in the data does lead to swelling in the resulting model estimate of primary and creep settlement. Despite this, the irreversibility so characteristic of peat oxidation is preserved in the inversion result. The derived contributions of the compaction processes can benchmark soil parameters or point to hitherto overlooked errors like incorrect prior information. The inversion can be expanded to encompass coupled groundwater flow and compaction models. This will improve the assessment of the effects of water management.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Data
  5. 3. Method
  6. 4. Results
  7. 5. Conclusions
  8. References
  • Iman, R. L., and W. J. Conover (1982), A distribution-free approach to inducing rank correlation among input variables, Commun. Stat., B11, 311334.
  • Koppejan, A. W. (1948), A formula combining the Terzaghi load-compression relationship and the Buisman secular time effect, Proc. Int. Conf. Soil Mech. Found. Eng. 2nd 1948, 3, 3234.
  • Muntendam-Bos, A. G., and P. A. Fokker (2008), Unraveling reservoir compaction parameters through the inversion of surface subsidence observations, Comput. Geosci., 13, 4355, doi:10.1007/s10596-008-9104-z.
  • Muntendam-Bos, A. G., I. C. Kroon, and P. A. Fokker (2008), Time-dependent inversion of surface subsidence due to dynamic reservoir compaction, Math. Geosci., 40, 159177, doi:10.1007/s11004-007-9135-3.
  • Tarantola, A. (2005), Inverse Problem Theory and Methods for Model Parameter Estimation, Soc. for Ind. and Appl. Math., Philadelphia, Pa.