Appendix

Naoyuki Yamashita

Theory of directional indicator semivariograms

The pattern of continuity of category sk can be characterized using semivariograms based

on indicator coding of the presence/absence of that category (Goovaerts 1997). Define

i (uα ; sk)={1if s (uα )=sk0otherwise

(Eq .1)

The indicator semivariogram for category sk is computed as

γ (h ;sk )= 12N (h)∑α=1

N (h)

[i (uα ; sk )−i(uα+h ;sk )]2(Eq.2)

where N(h) is the number of pairs at distance, h, andi (uα ; sk) is the category (0 or 1) of

interest at a location with coordinate uα. The indicator semivariogram value, γ(h; sk),

measures how often two locations, separated by vector h, belong to different categories, sk’

≠ sk. A better spatial connectivity of category sk is achieved when γ(h; sk) is smaller. γ(h; sk)

was calculated from 1-km mesh data (approx. 380,000 points for uα) for soil and bedrock

sensitivity. The pairs of N(h) were omnidirectionally searched within 150 km to determine

the effective distance (mesh size) between 1 km (soil and geological map) and 80 km

(CMAQ resolution). To determine the spatial-similarity of soil and bedrock sensitivity, a

measure of the joint variation of two continuous categorical attributes ski and skj is given by

the experimental cross-semivariogram:

γ ij (h; skij )=1

2N (h) ∑α=1

N (h)

[i (uα ; ski )− i(uα+h ;ski)] ∙ [ j (uα ;skj )− j (uα+h ; skj ) ](Eq .3)

If skj and ski are positively related, an increase in ski from uα to uα + h tends to be associated

with an increase in skj, which is calculated as an increase in γij (h ) (Goovaerts, 1999).

Okinawa and other isolated islands were not included in these analysis.

Variogram models were visually fitted to the experimental values of γ(h; sk)

(Goovaerts 1997). In this study, a spherical model with 2 or 3 spatial structures fit well.

1

γi (h )={bi0+bi

1[32 ( hai1 )−

12 ( hai1 )

3]+bi2[ 32 ( hai2 )−

12 ( hai2 )

3] for 0<h≤ai1

b i0+bi

1+b i2[3

2 ( hai2 )−12 ( hai2 )

3] for ai1<h≤ai2bi

0+bi1+bi

2 for ai2<h

(Eq .4)

where γi (h ) is the semivariance of categorical type i (soil or bedrock); b0i is the nugget

variance; b1i is the partial sill variance of the spherical first-range structure; and b2i is the sill

variance of the second-range structure. The superscripts (0, 1, 2) denote different spatial

scales. Eq. 3 shows the case of 2 spatial structures. The number of spatial structures was

determined visually. The nugget (b0), sill (b1, b2) and range (a1, a2) parameters were

determined by fitting this model, which characterizes the geometric pattern and effective

mesh size for the sensitivity of soil and bedrock.

2

Table S1

Naoyuki Yamashita

Interpretation of the soil type in “Fundamental Land Classification Survey map” by world reference

base for soil resources 2014 (IUSS Working Group WRB 2015).

Fundamental Land Classification Survey WRB 2014Sensitivity to

acidification

Alpine Lithosols Leptosol High

Lithosols Leptosol High

Residual Regosols Dystric Regosols High

Residual Regosols (including red yeallow soil) Dystric Regosols High

Volcanogeneous Regosols Regosols High

Volcanogeneous Regosols (including peat ash layer) Regosols High

Sand-dune Regosols Fluvisols High

Podozols (dry) Podzols High

Podozols (wet) Gleyic Podzols High

Brown Forest Soils (dry) Cambisols (Ochric) High

Brown Forest Soils (Slighty dry) Cambisols (Ochric) High

Brown Forest Soils Cambisols (Humic) Low

Brown Forest Soils (wet) Cambisols (Humic) Low

Red Soils Acrisols High

Yellow Soils Acrisols High

Dark Red Soils Acrisols (Rhodic) Low

Ando soils (coarse textured) Vitric Andosols Low

Ando soils (coarse textured, Kora and Masa) Vitric Andosols Low

Ando soils Andosols Low

Light Colored Ando soils Andosols Low

Gleyed Ando soils Gleyic Andosols Low

Blown Lowland Soils Gleysols Low

Gray Lowland Soils (coarse testured) Fluvic Gleysols Low

Gray Lowland Soils Fluvic Gleysols Low

Heavy clay soil Gleysols Low

Gley Soils (coarse textured) Gleysols Low

Gley Soils Gleysols Low

Peat Soils Dystric Histosols High

3

Table S2

Naoyuki Yamashita

Areal distribution (km2) among 5 risk categories in 8 administrative districts in the case F

map. Parentheses show the ratio of the risk area to all targeted areas (%).

　 Relative risk level (case F map) 　

　(Low)

I II III IV

(High)

VAll

Hokkaid

o24,800 22,000 10,000 12,400 800 70,000

(35) (31) (14) (18) (1) (100)

Tohoku 4,400 23,600 16,000 12,800 4,800 61,600

(7) (38) (26) (21) (8) (100)

Kanto 1,200 6,800 2,800 4,800 4,400 20,000

(6) (34) (14) (24) (22) (100)

Chubu 2,400 8,400 9,600 15,600 19,600 55,600

(4) (15) (17) (28) (35) (100)

Kansai 0 1,200 2,800 6,000 11,200 21,200

(0) (6) (13) (28) (53) (100)

Chugoku 0 800 2,800 3,600 19,600 26,800

(0) (3) (10) (13) (73) (100)

Shikoku 400 2,000 2,800 4,800 5,200 15,200

(3) (13) (18) (32) (34) (100)

Kyushu 0 9,600 5,600 4,000 7,600 26,800

(0) (36) (21) (15) (28) (100)

All 33,200 74,400 52,400 64,000 73,200 297,200

(11) (25) (18) (22) (25) (100)

4

Figure S1

Naoyuki Yamashita

(kmol ha-1 25y-1)(kmol ha-1 25y-1)

1.2 – 2.82.9 – 4.04.1 – 5.35.4 – 6.56.6 – 7.57.6 – 8.68.7 – 12.1

3.1 – 5.96.0 – 8.38.4 – 10.911.0 – 13.513.6 – 17.017.1 – 21.721.8 – 30.3

(a) (b)

Spatial distribution of cumulative S (a) and N (b) depositions on the Japanese archipelago

between 1981 and 2005.

5

Figure S2

Naoyuki Yamashita

b0

0.2

0.1

00 50 100 150a1 a2 a3

γ(h)

h (km)

b00.2

0.1

00 50 100 150a1 a2

γ(h)

h (km)

(a) (b)

b1 +

b2

b1 +

b2

+ b3

h (km)

γ(h)

0.2

0.1

050 100 150

(c)

a1 a2

The indicator semivariogram and the model of soil (a) and bedrock (b) sensitivity, and indicator cross-semivariogram of soil and bedrock (c). a1 - a3 and b0 - b3 show the parameters of semivariograms model.

6

Figure S3

Naoyuki Yamashita

(a) (b)

Sensitivity to acidification

LowHigh

Soil (a) and bedrock (b) sensitivity to acidification at 20km spatial scale. These mesh maps were aggregated from a soil and geological vector-map at the 1:500,000 scale. The aggregation size was determined from the ranges of indicator semivariograms for both variables.

7