Modeling of Bedrock Groundwater Levels Based on Antecedent Precipitation Indices
Ken'ichirou Kosugi
1,2,*
, Masamitsu Fujimoto
3
, Yosuke Yamakawa
4
Naoya Masaoka
1
, Tetsushi Itokazu
1
, Takahisa Mizuyama
1
1 Graduate School of Agriculture, Kyoto University,
2 CREST, JST
3 College of Science and Engineering, Ritsumeikan University
4 AFRC, University of Tsukuba
*Corresponding author. E-mail: kos@kais.kyoto-u.ac.jp
INTRODUCTION
Bedrock groundwater is reported to be one of the main factors governing occurrences of deep landslides. Hence, predictions of bedrock groundwater level (BGL) changes caused by rainwater infiltration are essential for assessments of the landslide vulnerability as well as for establishments of evacuation systems. This study proposed simple functional models which correlate antecedent precipitation indices (APIs) to BGLs.
METHOD
In the proposed models, BGLs are correlated with two APIs with two different half-life times (HLTs). Equation (1) assumes linear relationships between BGLs and APIs, and Eq. (2) employs power functions:
2 2 1 1
0 bX b X
b
H (1)
2 1
2 2 1 1 0
p
p b X
X b b
H (2)
where H is BGL observed from ground surface, X1 is API with a long HLT (M1), X2 is API with a short HLT (M2), and b0, b1, b2, p1, and p2 are parameters to be optimized. Performances of the models were examined by using an annual hydrograph of BGLs observed at a borehole excavated at a steep hillslope underlain by weathered granitic bedrocks.
RESULTS AND COCLUSIONS
Figures 1c through 1f indicated that, when HLTs were fixed at the ordinary values used for predictions of shallow landslides and debris flows (i.e., M1 = 72 h and M2 = 1.5 h), both of Eqs. (1) and (2) did not succeed in reproducing the observed BGLs. When HLTs were optimized, Eq. (1) produced better estimations with M1 and M2 values of 1077 and 30 h, respectively, both of which were much greater than the ordinary values (Figs. 1g and 1h). We could derive further improvements by optimizing HLTs in Eq. (2); that is, with M1 and M2
values of 1061 and 77 h, respectively, plots of Eq. (2) reproduced peaky response for each storm event as well as gradual seasonal variations of observed BGLs (Fig. 1i). On the optimized snake-line plots (i.e., Fig. 1j), H isopleths derived from Eq. (2) matched BGLs well.
We obtained similar results as shown in Fig. 1 for BGLs observed at 25 boreholes excavated at 5 different locations, and concluded that the power function model with two APIs is a suitable model for BGLs. The model can readily estimate BGLs anteceding and during storms and earthquakes which might trigger deep landslides. Moreover, it can be used for indicating the biggest BGL increases ever. Thus, the proposed model is effective for establishing evacuation systems against deep landslides and detecting vulnerable slopes.
Keywords: Deep landslide, bedrock groundwater, antecedent precipitation index
Fig. 1 (a, b) API, X1, with a long HLT of M1 and API, X2, with a short HLT of M2, and observed BGL and BGL computed by (c) Eq. (1) with fixed HLTs of 72 and 1.5 h, (e) Eq. (2) with fixed HLTs of 72 and 1.5 h, (g) Eq. (1) with fitted HLTs, (i) Eq. (2) with fitted HLTs, and (d, f, h, j) snake-line plots corresponding to each model calculation. In each snake-line plot, gray lines represent H isopleths derived by each equation.
Unit for H is meter.
b
X1 (mm) 0 200 400 600
X2 (mm) 0 50 100 150 200
a
X1 (mm) 0 50 100 150 200 250
X2 (mm) 0 10 20 30 40 50 60
Rain (mm/h)
0 20 40 60 80 100
c
3 4 5 6 7 8 9 10 11 12 1 2
Water level (m)
-15 -14 -13 -12 -11 -10
0 50 100 150 200
X2 (mm)
0 10 20 30
i
Month
3 4 5 6 7 8 9 10 11 12 1 2
Water level (m)
-15 -14 -13 -12 -11
-10 Observed
Computed
Sum of 1st and 2nd terms
X1 (mm)
0 200 400 600 800
X2 (mm)
0 50 100 150 200
g
3 4 5 6 7 8 9 10 11 12 1 2
Water level (m)
-15 -14 -13 -12 -11 -10
0 200 400 600 800
X2 (mm)
0 40 80 120 160
0 50 100 150 200
X2 (mm)
0 10 20 30
d
j f
Observed
h
Computed
Sum of 1st and 2nd terms
e
3 4 5 6 7 8 9 10 11 12 1 2
Water level (m)
-15 -14 -13 -12 -11 -10
Observed Computed Observed Computed
H < -14.5 m -14.5 ~ -13.5 -13.5 ~ -12.5 -12.5 ~ -11.5 H > -11.5 m
-13.5 -11.5 -12.5 -14.5
-11.5 -12.5
-13.5
-14.5
-11.5 -12.5 -13.5 -14.5
-11.5 -12.5 -13.5
-14.5
Color scale for d, f, h, and j
X1(M1= 1061.3 h) X2
(M2= 76.8 h) X1(M1= 72 h)
X2(M2= 1.5 h)
