CGI2024 manuscript No.
(will be inserted by the editor)

Seasonal Terrain Texture Synthesis
via Köppen Periodic Conditioning
Toshiki Kanai · Yuki Endo · Yoshihiro Kanamori

Apr.

May

Oct.

Aug.

Mar.

Fig. 1 3D terrain models textured using our method. Our method can generate terrain textures that reflect climatic andseasonal changes using a heightfield and monthly temperature, precipitation, and insolation as inputs. (Top) Textures forApril and October in the frigid zone. (Middle) Monthly changes from April to October. (Bottom) 3D models (with a different
heightfield) generated using typical textures for (left) torrid, (center) subarctic, and (right) frigid zones, respectively.

Abstract This paper presents the first method forsynthesizing seasonal transition of terrain textures for
an input heightfield. Our method reproduces a seamless
transition of terrain textures according to the seasonsby learning measured data on the earth using a convolutional neural network. We attribute the main seasonal
texture transition to vegetation and snow, and control
the texture synthesis not only with the input heightfield
but also with the annual temperature and precipitation
based on Köppen’s climate classification as well as insolation at the location. We found that month-by-month
T. Kanai
E-mail: kanai.toshiki.as@alumni.tsukuba.ac.jp
University of Tsukuba
Y. EndoE-mail: endo@cs.tsukuba.ac.jp
University of Tsukuba
Y. Kanamori
E-mail: kanamori@cs.tsukuba.ac.jp
University of Tsukuba

synthesis yields incoherent transitions, while a naı̈ve
conditioning with explicit temporal information (e.g.,month) degrades generalizability due to the north-south
hemisphere difference. To address these issues, we
introduce a simple solution – periodic conditioning on
the annual data without explicit temporal information.
Our experiments reveal that our method can synthesize
plausible seasonal transitions of terrain textures. We
also demonstrate large-scale texture synthesis by tilingthe texture output.
Keywords Deep learning · GAN · Texture synthesis ·Terrain

1 Introduction
We can see a wide range of earth landscapes due toterrain and climate variations. The landscape appearance can also change dramatically with seasons, even in
the same location. For example, in regions with large

2temperature differences between summer and winter,such as subarctic regions, trees are in full leaf in summer
and snow in winter. Suppose we can reproduce theseappearance differences due to terrain, climate, andseasonality in a 3D terrain model. We can then explore
a wide range of applications in fields such as video andgaming productions and in visualizing the impact of
global warming and other climate change effects on
the earth. However, existing studies on terrain andlandscape in computer graphics have mostly focusedon the generation of 3D terrain geometry [19, 44, 20,
41,11, 24, 35, 18], with relatively little attention paid toterrain texture synthesis [42, 43]. In particular, to thebest of our knowledge, there are currently no methods
for generating terrain textures that take into accounttransitions due to climate and season.
The terrain texture variations due to climate
and seasonality are mainly caused by vegetation andsnow. Regarding vegetation, Köppen’s climate classification [34] focuses on differences in vegetation, whichuses temperature and precipitation as explanatory variables to classify climate. For snow, the terrain geometry
affects snow accumulation and melting; for example,
snow tends to accumulate more and melt more slowly
in highlands. Also, in the north hemisphere for example,
south-facing slopes receive more sunlight, so snow
accumulates more slowly and melts more quickly thanon north-facing slopes. Other factors that affect climate
and season include, for example, latitude. However, various places with different latitudes have similar climates
due to the influence of ocean currents. Therefore, latitude is not an appropriate control parameter for climate
and season. Based on these considerations, we propose
a method for generating terrain textures that reflect
climate and season using a heightfield and monthly
temperature, precipitation, and insolation for one year
as inputs. By using a convolutional neural network(CNN) trained with our novel measured dataset, we cansynthesize terrain textures in all seasons for the input
terrain heightfield (see Figure 1).
This study aims to address the following two issues.
First, the generated terrain textures should not dependon month information, such as “February is winterand August is summer,” because seasons may differ
even in the same month, for example, in the northernand southern hemispheres. Furthermore, suppose alocation on a hemisphere has a terrain geometry andannual temperature and precipitation similar to thoseon the other hemisphere with a half-year delay forthe annual data. These locations should have similar texture transitions; as proof, Köppen’s climateclassification does not depend on month information.
Second, there is no available dataset of heightfields with

Toshiki Kanai et al.

ground-truth terrain textures that include temperatureand precipitation information, which is necessary forthe supervised training of our network.
This paper offers the following simple solutions.
For the first issue, we control the temporal texture
transition by ordering the input monthly data, i.e., temperature, precipitation, and insolation. Namely, we synthesize terrain textures for one year month-by-monthwhile changing the order of the annual data periodicallyso that the target month’s data come first. We refer toour technique as Köppen periodic conditioning, whichyields better generalizability across the north and south
hemispheres. We offer smooth inter-month transition
via feature map interpolation. For the second issue,
we construct a novel dataset combining measured datafrom multiple data sources such as space shuttles andsatellites. As no competitive methods exist, we validate
the effectiveness of our method through an ablation
study comparing several variants with different inputs,
such as latitude and explicit month information. We
further demonstrate large-scale texture synthesis bytiling texture outputs.

2 Related Work
3D terrain generation. A number of terrain generation methods have been proposed to support the
production of 3D terrain models [14], with a particularfocus on heightfield generation. For example, Guérin etal. [19] trained a CNN on the space shuttle 3D terrain
data (NASA SRTM) to generate a realistic heightfieldfrom a sketch. In a recent study by Guérin et al. [20],a multigrid method can also be used to interactively
generate heightfields by converting gradient manipulations from sketch input to elevation values in realtime. However, these methods do not generate terrain
textures corresponding to the heightfields.
Terrain appearance simulation. Vegetation andsnow cover are two of the most important elements forrepresenting seasonally changing landscapes. For vegetation, computer graphics has a long history of researchon plant growth simulation and modeling [17, 27, 4, 36,
22, 5]. Makowski et al. [25] focused on the relationshipbetween temperature and precipitation as a means ofcontrolling models of vegetation ecosystems and incorporated these as parameters in their simulations. Palubicki et al. [29] built on these geographic parameters toallow for more microscopic vegetation simulations. In
snow cover simulations, solar radiation is also used as
an environmental information other than temperatureand precipitation [13, 10]. A similar study [3] used solar

Precipitation

Temperature

60[℃]
40
20

-40

Conv

ConcatC

Conv

Temperature

1 2 3 4 5 6 7 8 9101112

Concatenated input
for month mConcatenated input
for month m

KPD
ResBlk

KPD
ResBlknv

βmInsolation Heightfield

γm

400
300

Instance
Norm

200

Precipitation

3Co

500[mm]

0
-20

month
(m+1)
(m)
month
month m

month
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(m)
month mmonth
(m+10)(m+10)
month

month
(m+1)
(m)
month
month mmonth
(m+10)

Seasonal Terrain Texture Synthesis via Köppen Periodic Conditioning

100
0User inputs for month mMultiply Add(Element-wise)

Köppen Periodic Denormalization (KPD)

KPD ResBlk: Replacement of SPADE ResBlk with our
Köppen Periodic Denormalization (KPD)

Our network architecture

Terraintexturefor month m

Fig. 2 Overview of our method. To output a terrain texture for month m (where m = 1, 2, . . . , 12), one-year temperature,
precipitation (both represented as constant maps), and insolation maps are ordered (where M(i) = (i mod 12) + 1),
concatenated with the target heightfield (left), and fed to the Köppen Periodic Denormalization (KPD) layer (middle). The
concatenated input for month m is injected repeatedly at multiple scales (right). One-year textures are generated by repeating
the whole process for each month m. Note that heightfields in this paper are visualized using linear normalization for better
display.

irradiance in glacier simulations. Argudo et al. [2] proposed a method to generate a variety of ground surface
conditions, taking into account both vegetation andsnow cover. Their method constructs a coherent multilayer dictionary that represents relationships amongparameters such as topographic elevation, vegetation
density, and irradiance. These simulation methods can
produce photorealistic scenes with snow or vegetation.
However, they cannot handle seasonal changes over anannual cycle, taking into account both vegetation andsnow cover. In addition, although our work is similar
to theirs in that they use various geographic data, ourproblem setting differs from their works in that our goal
is to obtain topographic textures.
Terrain texture synthesis. Terrain textures arealso used to represent large-scale topography andfor geospatially based artworks such as panoramic
maps [37, 7]. The existing study on terrain texture
generation by Spick et al. [42] can generate four-channel
textured heightfields via supervised learning using
CNNs. Zhu et al. [45] proposed a method to generate
satellite images from the labeled map data. Panagitou
et al. [30] presented a framework for generating bothterrain textures and heightfields using generative adversarial networks (GANs). However, these methods do
not account for seasonal transitions in terrain texturesand do not allow user control over the generated
heightfields and terrain textures.
Dachsbacher et al. [12] proposed a method forgenerating terrain textures using geographic data on
temperature, precipitation, and solar radiation, in addition to heightfields. This method classifies each pixel
as rock, vegetation, water, or snow based on the given
geographic data, and colors it according to the classification result. However, such a method suffers fromthe problem of representing colors that continuously
change with the seasons. In addition, this method
requires pixel-by-pixel temperature and precipitation
maps, but it is costly for the user to prepare such
input. Although such parametric or rule-based texture
generation methods are often effective for generating
textures at a specific time instance, they are difficult tocontrol for continuous transition. Our method, on theother hand, can generate smooth time-varying terrain
textures with a simple control using temperature andprecipitation.

Image-to-image translation. Image-to-image translation techniques have evolved rapidly with the adventof U-net [39], GANs [15] and diffusion models [21]. A
wide variety of methods [31] exist, such as pix2pix [23],
SPADE [32], and Palette [40] for supervised learningof transformations between domains, CycleGAN [46]for unsupervised learning, and BicycleGAN [47] andSwapping Autoencoder [33] for multimodal transformations. These methods have also been used to reproduce
seasonal changes such as summer to winter. However,in order to create terrain textures that account forvarious climates and seasons, users need to prepare
multiple reference images in advance. In our study, by
focusing the extensibility of the SPADE’s denormalization layer [32], we extend it and introduce a novel
denormalization layer that processes heightfields andmonthly temperature, precipitation, and insolation for
one year. This allows the generation of a variety ofterrain textures reflecting climates and seasons without
the use of reference images.

Toshiki Kanai et al.

Figure 2 summarizes our method. Our inputs are aheightfield and monthly temperature, precipitation,and insolation data for one year. We train a CNN
in a supervised manner to synthesize terrain texturesreflecting the corresponding climate and season. As the
CNN architecture, we extend the spatially denormalization layer (SPADE) by Park et al. [32] for our purpose.
Whereas the original SPADE block accepts a semantic
mask to enforce spatial layout for photorealistic semantic image synthesis, there are several extensions ofdenormalization layers for handling geometric information [26, 38], optical flows [26], and shadow removal fromterrain landscapes [43]. We adopt a denormalization
layer to inject information on heightfield, temperature,
precipitation, and insolation at multiple scales. For
training, because there is no dataset for our purpose,
we create a novel dataset using the geospatial analysis
platform Google Earth Engine [16]. Hereafter we explain the details of conditioning with denormalization
layers and dataset construction.

Input for month m

3 Our Method

Conv

Input for month m+1

4

Conv

Co
n

v

Conv

βm+1

Co

×t

nv

γm+1

Conv

×t

βm
γm

× (1 - t )× (1 - t )Instance
Norm

Element-wise

Fig. 3 Feature map interpolation between consecutive
months. The feature maps {β, γ} for months m and m + 1
are linearly interpolated with parameter t ∈ [0, 1] and thenfed to the denormalization block.

channel direction, and then fed to our Köppen Periodic
Denormalization (KPD) block (Figure 2, middle).

3.1 Conditioning in Denormalization Layer
3.2 Network Design and Extensions
We aim to synthesize a terrain texture for each monthfrom the inputs (and later employ inter-month interpolation in Section 3.2). A straightforward way
would be to feed just one month of information andoutput a texture month-by-month, just like an ordinary image-to-image translation. Unfortunately, thisapproach yields temporally inconsistent textures, as wedemonstrate later in Section 4.2. Instead, we feed one
year of information to our network to account for theannual transition. In this case, a natural question is
how we can signal the target month’s information to
the network. A naı̈ve approach would be to feed thetarget month’s index to the network explicitly, but thisapproach does not generalize across the north and south
hemispheres, as explained in Section 1.
Our solution is to rotate the one-year data periodically so that the target month’s data come tothe front (Figure 2, left). More formally, suppose wewant to synthesize a texture for month m (wherem = 1, 2, . . . , 12). We order each of the annual temperature, precipitation, and insolation according to thesequence of {m, M(m), M(m + 1), . . . , M(m + 10)},where M(i) = (i mod 12) + 1. For example, in thecase of October (i.e., m = 10), the sequence becomes{10, 11, 12, 1, . . . , 9}. The sequences of temperature andprecipitation are converted into constant maps of thesame size as the input heightfield, concatenated together with the insolation maps and heightfield in the

Network architecture and loss functions. Our networkarchitecture is a simple extension of that of SPADE [32].
Namely, we replace the SPADE residual blocks (orResBlk) with our KPD ResBlk (Figure 2, right), where
the SPADE blocks are replaced with our KPD blocks.
We use the same loss functions as those of the SPADE
network, except that we omit the loss for the variational
autoencoder (VAE) because we do not use VAE.

Feature map interpolation for inter-month texture transition. So far, we can generate monthly terrain textures, but it is important to be able to handle continuous seasonal changes between months when considering
applications such as video production. Our method
can obtain continuously changing terrain textures byinterpolating the feature maps. Specifically, during inference, the feature maps {βm , γm } and {βm+1 , γm+1 }in our KPD block for months m and m + 1 are linearlyinterpolated with parameter t ∈ [0, 1] (Figure 3).
β ′ = (1 − t) βm + t βm+1 ,γ ′ = (1 − t) γm + t γm+1 .
(1)The interpolated {β ′ , γ ′ } are then used in our KPD
block.

Seasonal Terrain Texture Synthesis via Köppen Periodic Conditioning

3.3 Dataset
We construct a dataset for training using the geospatial analysis platform Google Earth Engine [16]. Our
dataset consists of four types of observational data
and two types of derived data. The observational data
are heightfields, corresponding monthly temperatureand precipitation data for one year, and terrain textures, all observed in 2020 and publicly available.
The heightfields are obtained from NASADEM [28],and the spatial resolution is 30 meters per pixel. For
temperature and precipitation, we use the monthly
averaged data of ERA5 [9]. Our terrain textures are
the Level-2 product of the Sentinel-2 land observation
satellite [1], in which atomospheric effects (e.g., faintclouds) and terrain shadings are removed to someextent. The spatial resolution is 10 meters per pixel.
Our derived data are cloud masks and insolation maps.
Cloud masks are binary masks to specify clouds andcloud shadows in the terrain textures; although thesatellite images were taken by two satellites every fivedays, cloudy sites might often be covered by clouds
with their shadows. We thus synthesize terrain texturesfrom one-month satellite images with minimum clouds
and shadows, which are extracted as cloud masks [6].
To eliminate the effects of clouds and shadows during
training, we exclude them in calculating loss functions
using the cloud masks. Before subdivided into 256×256
tiles, the insolation maps are calculated by averaging
the direct solar radiation for every hour for the 15th
day of every month using ray casting, considering thesolar positions at specific longitudes1 .
Our dataset includes 97 sites randomly sampledfrom land territories while excluding artificial structures. The sampled sites are categorized according toKöppen’s climatic divisions as follows: A (torrid) 13
sites, B (arid) 32 sites, C (temperate) 27 sites, D(subarctic) 15 sites, and E (frigid) 10 sites. A totalof 10 sites, two randomly selected from each of thefive climate categories, were used as test data, andthe remaining 87 sites were used as training data.
Each site was sampled at 0.5 degrees latitude andlongitude, and the resulting image data has a resolutionof 5, 500 × 5, 500 pixels and was divided into small tilesof 256×256 pixels. We also excluded the following sites;
1) sites with elevations less than 100 meters, which
tend to contain artificial structures, and 2) sites withmissing areas in the terrain texture that exceeded five
percent of 256 × 256 pixels (e.g., the gray boxes in the
ground-truth (GT) textures in Figure 6). Note thatthe black pixels in the GT textures of Figures 6 and1

We used pvlib for calculating the solar altitude from thelatitude.

5

7 are missing areas due to clouds. Consequently, thedataset contains 414K terrain textures and 41K heightfields at a resolution of 256 × 256 pixels. We matched
the resolutions of heightfields and insolation maps tothat of terrain textures (i.e., 256 × 256) using linear
interpolation, whereas we used averaged temperatureand precipitation values within each heightfield.
Note that all the climate categories to which eachsite belongs are based on the study by Chen et al. [8].
Because temperature and precipitation vary somewhat
from year to year, the combinations of climate divisions
and temperature/precipitation in this paper do notnecessarily correspond to the definition of each climate
division.

4 Results
4.1 Experimental Setting
We implemented our method using Python and PyTorch and ran on an NVIDIA RTX A6000 for training
and inference. The Adam optimizer was used with alearning rate of 0.0002 and (β1 , β2 ) = (0, 0.999), respectively. The batch size used was 32, and the model wastrained for 20 epochs, which took approximately fourdays. The results reported are based on the test dataand not the training data. Some values of temperatureand precipitation in the dataset are fictional.
To validate our method, as there are no existing
methods with the same objective, we conducted anablation study by comparing it with different conditions. We denote temperature as T, precipitation as P,
month index as M, latitude as L (where T, P, M, andL are represented as constant maps whose resolution
is 256 × 256), and insolation maps as S. We omit
heightfield symbols to shorten the descriptions because
all conditions require heightfields. In the following experiments, the resolution of output textures is 256×256
pixels and the spatial resolution is 10 meters per pixel.
Condition 1 (T′12 + P′12 + M): We fed a heightfield,
fixed-ordered temperature T′12 and precipitation
P′12 for one year, and month index M.
Condition 2 (T1 + P1 ): We fed a heightfield, onemonth temperature T1 and precipitation P1 .
Condition 3 (L + M): We fed a heightfield, latitudeL, and month index M. The latitude L is anapproximation of average insolation.
Condition 4 (T12 + P12 ): We fed a heightfield, andperiodically-rotated temperature T12 and precipitation P12 for one year (as explained in Section 3.1),
without insolation maps S.

6Toshiki Kanai et al.
(b)

(c)

(d)

texturesheightfields

inputs

(a)

(a)

(b)

(c)

(d)

1

2

3

4

5

6

7

8

9

10

11

12

Fig. 4 Qualitative comparison of terrain textures generated by changing only the input heightfields. We generated the 3D
terrain models using the terrain textures in the red rectangles and the input heightfields. The result texture patterns differ
depending on the terrain shapes.

(a)

...

...

(b)

...

...

inputsFig. 5 Qualitative comparison of terrain textures obtained via (a) output image interpolation and (b) feature mapinterpolation. The terrain turns uniformly white in (a), while the snow increases gradually from top to bottom in (b).

Ours (T12 + P12 + S12 ): We fed a heightfield, and periodically-rotated temperature T12 , precipitation
P12 , and insolation S12 for one year.
The input maps are concatenated in the channel direction.
4.2 Qualitative Evaluation
Comparison of Conditions 1-4 and Ours. Figure 6
shows a qualitative comparison of Conditions 1-4 andour method. The top results show that Conditions 1
and 3 are poorly reproducible throughout the year.
Condition 2 exhibits an extreme decrease in vegetationfrom March to June. Condition 4 and our method
produced textures that reflected consistent seasonalchanges that were close to the ground truth throughout
the year. In the lower results, Condition 1 produced
dry textures. In Condition 2, the change from Juneto September is extreme. In Conditions 3 and 4, theseasonal changes are continuous but poorly reflect
summer vegetation. Our method produced texturesthat were closer to the ground truth than the otherconditions. The black area in the ground truth is themissing area where the image of the ground surface
could not be obtained.

Verifying adaptability to input periodicity. We verified
that our method depends not on month indices but only
on the temperature and precipitation transitions toreflect seasonal texture differences. Figure 7 compares
Condition 1 (T′12 + P′12 + M) and Condition 4 (T12 +P12 ), feeding temperature and precipitation with ahalf-year delay. Condition 1 relies on month indicesand cannot account for the temperature and precipitation periodicity to generate photorealistic textures,
exhibiting almost blue-or-white with grid-like artifacts.
Condition 4 successfully handles the same temperatureand precipitation transitions despite the half-year delay.
Note that the quantitative assessment in Table 1 does
not reflect these extreme differences because there isless land in the southern hemisphere and, therefore, lesssouthern hemisphere data in the dataset.

Seasonal Terrain Texture Synthesis via Köppen Periodic Conditioning
Table 1 Quantitative comparison of the different input
conditions. The bold and underlined values show the bestand second-best scores.
RMSE ↓ SSIM ↑ LPIPS ↓ ∂AD↓′′

Cond. 1 (T12 + P12 + M)
Cond. 2 (T1 + P1 )Cond. 3 (L + M)
Cond. 4 (T12 + P12 )Ours (T12 + P12 + S12 )

64.3
75.7
66.8
61.1
59.3

0.57
0.52
0.55
0.52
0.52

0.47
0.49
0.46
0.44
0.44

123.3
124.8
116.9
120.8
123.3

∂SSIM↓
0.13
0.16
0.14
0.11
0.11

Verifying input dependency. Figure 8 shows qualitative
comparisons with varying input temperature and precipitation, respectively. The continuous changes in theterrain textures with the varying input temperatureand precipitation confirm that our method can synthesize textures that reflect climate and seasons. For
example, in July, the cooler the temperature and thehigher the precipitation, the greener the vegetation. In
October and November, colder temperatures and more
precipitation lead to more snow accumulation.
Figure 4 shows qualitative comparisons with varying
input heightfields. Even with the same temperatureand precipitation input, the resultant textures differ fordifferent terrain shapes. It can be seen that heightfields
play an important role in texture synthesis.
Verifying feature map interpolation. Figure 5 shows acomparison between the results of linear interpolation
at (a) the output texture level and (b) the feature map
level (explained in Section 3.2), to obtain continuous
seasonal transition between two adjacent months in thewinter season with snow cover. (a) The output texture
interpolation does not take elevation into account andshows only a simple hue change. Contrarily, (b) the feature map interpolation shows the plausible progressionof snow cover from higher elevations.

4.3 Quantitative Evaluation
For quantitative evaluation with reference to theground-truth textures, we adopt RMSE, SSIM, andLPIPS as evaluation metrics. To evaluate the validityof the seasonal transitions, we also define novel metrics,
i.e., ∂AD and ∂SSIM, which are defined as follows:∂AD = E [||Gm+1 − Gm | − |Tm+1 − Tm ||] ,(2)∂SSIM = E [|SSIM(Gm+1 − Gm ) − SSIM(Tm+1 − Tm )|] ,(3)
where m is a month index, G is a ground-truth texture,
and T is an inferred texture.
Table 1 shows the result of quantitative comparison
with different input conditions. As can be seen in
the table, Ours won the most frequently. Although

7

Conditions 1 and 3 scored the best for SSIM and ∂AD,
respectively, these conditions show much worse RMSE,
which consequently results in low-quality textures, as
discussed in Section 4.2. Note that the inconsistentscore rankings among the evaluation metrics in Table
1 stem from the different characteristics of the metrics
and resultant images, which is common in evaluationsof machine learning techniques. Further investigation isleft for future work.

5 Discussions
This study aims to generate seasonal changes inmountainous regions, taking into account vegetationand snow cover. Our method uses temperature andprecipitation as environmental information based on
the Köppen’s climate classification and also considers
insolation. Insolation contributed to the accuracy, especially when generating snowy textures for subarctic andarctic zones distributed at high latitudes. This may be
due to the fact that, in high-latitude regions, the annual
sun elevation changes significantly, and when the sun islow, there is a clear distinction between slopes exposed
to direct sunlight and those that are not, resulting indifferences in ground surface temperature.
We discuss the controllability of our method. Our
method can generate various terrain textures from thecorresponding user inputs. Heightfields can be obtained
from existing DEM data or created using existing tools.
The temperature and precipitation data can be selectedfrom typical data of climatic divisions with additional
modification if necessary. The insolation maps can becalculated automatically, as mentioned in Section 3.3.
We do not rely on pixel-level temperature/precipitation
maps because we have to employ physics simulations
to obtain such maps, considering other factors, suchas wind and pressure, which drastically deteriorates
usability. We can also handle large-scale scenes by
seamlessly connecting adjacent texture tiles, as demonstrated in Figure 1 (see Appendix A for the details).

6 Conclusions and Future WorkIn this paper, we have for the first time addressed theterrain texture generation that can control seasonaltransitions for an input heightfield. To achieve this, we
proposed a supervised learning framework using a CNN
that includes monthly temperature, precipitation, andinsolation as conditional signals. Our method can appropriately reflect seasonal transitions of the generated
terrain texture by periodically changing the input orderof monthly temperature, precipitation, and insolation.

8

In addition, we created a novel dataset based on actual
observations from space shuttles and satellites to train
the CNN. The experiments showed that our method
can generate realistic terrain textures corresponding to
the input signals.
As a future challenge, we would like to improve theaccuracy of terrain texture generation in areas withheavy rainfall, in particular, the torrid zones. Somesatellite images for the torrid zones contain thin clouds
that could not be removed. Higher quality datasets
produced through the further development of remotesensing technology will improve the resultant quality.
Our inputs and outputs have a one-to-one correspondence and have no randomness. This design was madebecause simply adding randomness would degrade thequality of the generated terrain textures. To account forvarious factors not considered in the input conditions, it
might be useful to introduce some randomness to enrich
the output variations. In particular, an interesting
avenue of future work is to integrate our periodic
conditioning into the modern architectures of diffusion
models to explore output variations.

Acknowledgement
The authors are grateful to Prof. Kenichi Ueno for his
professional feedback on climate science.

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A Large-scale Texture Synthesis by Tiling
Outputs
To obtain a large terrain texture corresponding to a heightfield larger than the input/output resolution (i.e., 256 ×256) of our texture generation CNN, we seamlessly connect
adjacent output textures using alpha blending. We divide an
input heightfield into small tiles of 256 × 256 pixels with a
stride of 128 pixels and feed them to the texture generation
CNN to obtain small texture tiles corresponding to eachheightfield tile. To blend the neighboring texture tiles, we
blend the quarters (i.e., 128 × 128 pixel regions) of eachtexture tile, which are covered by four neighboring tiles except
for the heightfield boundaries. By applying an alpha map
whose alpha values are defined by normalized distances fromthe center pixel, we can obtain a large terrain texture without
noticeable seams. Figure 1 shows the rendered result withan alpha-blended texture corresponding to a heightfield ofapproximately 5, 500 × 5, 500 pixels. For the temperature andprecipitation in generating large-scale terrain textures, theuser can choose whether to specify them on a per-tile basis
or to use a constant value for the entire area, depending on
the quality desired by the user. In the result of Figure 1,
the temperature is varied by −0.6◦ C per 100m elevationdifference (standard temperature reduction rate) between theentire elevation average and the per-tile elevation average.
While we used the same value for precipitation for simplicity,
high-quality textures were obtained.

(bottom)Toshiki Kanai et al.

(top)

inputs10Jan.

insolation

Jul.

Jan.

temperature (red)heightfieldand precipitation (blue)Jul.

insolation

Ours

Cond. 4

(L 20)
Cond. 3

Cond. 2

Cond. 1temperature (red)heightfieldand precipitation (blue)

GT

N/A
2

3

4

5

6

7

8

9

10

11

12

Ours

Cond. 4

(L 50)
Cond. 3

Cond. 2

Cond. 1

1

GT

N/A
1

2

3

4

5

6

7

8

9

10

11

12

Fig. 6 Qualitative comparison of terrain textures obtained by Conditions 1-4 and our method. The black pixels in the GT
texture are missing areas due to clouds. The grey boxes with “N/A” indicate that the textures were excluded from the dataset
due to the high deficiency level. See Section 3.3 for the details.

(top)

GT

Cond. 4

Cond. 1

GT

Cond. 4

Cond. 1

inputs11(bottom)

Seasonal Terrain Texture Synthesis via Köppen Periodic Conditioning

1

2

3

4

5

6

7

8

9

10

11

12

Fig. 7 Qualitative comparison of terrain textures obtained by Conditions 1 and 4 for contrasting the conditioning using
month index maps (Condition 1) and our periodic conditioning (Condition 4). The black pixels in the GT texture are missing
areas due to clouds.

Toshiki Kanai et al.

inputs12

temperature (red)and precipitation (blue)Jul.

heightfield

insolation

Nov.

+5℃

+0℃

GT

-5℃

1

2

3

4

5

6

7

8

9

10

11

12

1

2

3

4

5

6

7

8

9

10

11

12

+30mm

+0mm

GT

-30mm

Fig. 8 Qualitative comparison of terrain textures generated by changing only the input temperature or precipitation. As
shown in the red rectangles, the lower temperatures and higher precipitation increase the white areas due to snow cover inearly spring in April. The higher precipitation also makes the green colors of the vegetation deeper in August, in summer.