The Zonation of Mountain Frozen Ground under Aspect Adjustment Revealed by Ground-Penetrating Radar Survey—A Case Study of a Small Catchment in the Upper Reaches of the Yellow River, Northeastern Qinghai–Tibet Plateau

Abstract

Permafrost distribution is of great significance for the study of climate, ecology, hydrology, and infrastructure construction in high-cold mountain regions with complex topography. Therefore, updated high-resolution permafrost distribution mapping is necessary and highly demanded in related fields. This case study conducted in a small catchment in the northeast of the Qinghai Tibet Plateau proposes a new method of using ground-penetrating radar (GPR) to detect the stratigraphic structure, interpret the characteristics of frozen ground, and extract the boundaries of permafrost patches in mountain areas. Thus, an empirical–statistical model of mountain frozen ground zonation, along with aspect (ASP) adjustment, is established based on the results of the GPR data interpretation. The spatial mapping of the frozen ground based on this model is compared with a field survey dataset and two existing permafrost distribution maps, and their consistencies are all higher than 80. In addition, the new map provides more details on the distribution of frozen ground. In this case, the influence of ASP on the distribution of permafrost in mountain areas is revealed: the adjustment of ASP on the lower limit of continuous and discontinuous permafrost is 180–200 m, the difference in the annual mean ground temperature between sunny and shady slopes is up to 1.4–1.6 °C, and the altitude-related temperature variation and uneven distribution of solar radiation in different ASPs comprehensively affect the zonation of mountain frozen ground. This work supplements the traditional theory of mountain permafrost zonation, the results of which are of value to relevant scientific studies and instructive to engineering construction in this region.

1. Introduction

The most extensive high-altitude permafrost region in the middle and low latitudes of the Northern Hemisphere occurs on the Qinghai–Tibet Plateau (QTP) [1]. According to the geomorphology of the QTP, the high-altitude permafrost can be distinguished into two sub-classes: high-plain permafrost and mountain permafrost [2]. The development and spatial distribution of permafrost greatly affect the ecosystem and regional hydrological process in cold regions, inducing geological disasters and affecting human infrastructure [3,4,5]. The situation may be more serious in the mountain permafrost regions on the QTP, especially when driven by climate change [4]. Thus, the distribution and evolution of mountain permafrost and its environmental effects have attracted more and more attention from scientists [3,6,7].

In recent decades, the air temperature (+0.036 °C/yr) and land surface temperature (+0.03 °C per year) on the QTP have been rising very quickly [8], far exceeding the average increase in the global land surface temperature (+0.011 °C/yr) [9]. The average increasing rate for the ground temperature at a 6 m depth was 0.043 °C per year between 1996 and 2006 [10], and the latest results show that the mean warming rate for the ground temperature at a 10 m depth had reached approximately 0.025 °C per year (2004–2018) in permafrost regions on the QTP [11]. In mountain permafrost regions, the effect of climate warming is superimposed on the effect of complex topography, which leads to increased uncertainty in the assessment of the variations of permafrost distribution [12]. Some studies have shown that the permafrost types and distribution are closely related to ecological characteristics, and permafrost degradation will lead to the destruction of the original hydrothermal state and, thus, result in a succession of ecosystems [13,14]. The permafrost degradation also influences the hydrologic process in mountainous areas, the flood peak (during the thawing season) will decrease, and the runoff during this recession will increase significantly, along with permafrost thawing [15]. Meanwhile, permafrost degradation will weaken the stability of mountain slopes and increase the risk of rock falls, landslides, and other geological disasters [3,16,17].

In order to further explore the ecological, hydrological, and disaster effects of permafrost in mountain regions, the detailed distribution of mountain frozen ground is necessary and highly demanded. The permafrost distribution can be conceptualized with the regional climate, topography, and ground conditions [6]. In mountain regions, rugged and complex terrain will alter and regulate the regional climate background and ground-surface conditions, thus playing a more critical role in the formation and distribution pattern of mountain permafrost than in areas with relatively flat terrain. A study showed that topography and surface conditions can affect the annual mean ground surface temperature (MAGST) by as much as 15 °C over a distance of 1 km [6], which leads to a high spatial heterogeneity of frozen ground distribution in mountain areas.

At present, a number of permafrost distribution maps on the QTP with different scales have been produced in different ways, which include: (1) traditional manual mapping based on field surveys and reference data [2]; (2) mapping with human–machine interactive image interpretation methods involving GIS technology and remote sensing data [2]; (3) with physical or semi-physical models driven by spatio-temporal data [18,19,20]; and (4) with statistics or machine learning models driven by multivariate data [21,22,23], etc. However, almost all of the work has exposed the issue of insufficient field-measured data on the plateau. Especially for mountainous areas, the fine and accurate descriptions and mapping of permafrost distribution are still far from enough [24,25,26,27,28,29] and cannot meet the needs of practical regional studies, e.g., hydrological modeling, ecological evolution assessment, or guidance for the design and construction of infrastructure, e.g., road construction [29]. Therefore, high-resolution and updated maps of frozen ground distribution in mountainous regions are always in demand. The premise of achieving this goal is to obtain a large quantity of more effective field survey data.

Ground-penetrating radar (GPR) is an efficient, non-destructive tool for detecting subsurface structures [30]. The difference in the dielectric constant between the target object and the surrounding geological body is the premise of GPR detection [31]. In permafrost regions, there is generally a difference in the dielectric constant between frozen and thawed soil, which leads to continuous, strong-amplitude, and in-phase reflection signals appearing on the GPR image at the corresponding position of the freeze–thaw interface [30]. Therefore, GPR has been widely used in the identification of permafrost-related features, such as the presence of permafrost [30,32,33,34,35], seasonal thawing depth or active-layer thickness [30,36,37,38,39,40,41], active-layer moisture regime [38,42], and the condition of ground ice [42,43,44,45], etc. However, there are few applications with which to extend the results of GPR detection from a local scale to a regional scale.

In this study, we tested a new method to establish an empirical–statistical zonation model of permafrost based on the interpretation results of GPR survey data and produced a regional distribution map of frozen ground in the small catchment of the Qushian River, a tributary of the Yellow River. The aims of the study are as follows: (1) to verify the applicability and performance of a GPR survey in the study of permafrost distribution in mountainous areas; (2) to propose an improved scheme of permafrost zonation, taking into account the aspect (ASP) adjustment, and generate the high-resolution permafrost distribution map of the concerned area; (3) to evaluate the generated permafrost map; (4) to quantify and explain the influence of ASP; and other factors on the zonation and distribution of mountain permafrost.

2. Materials and Methods

2.1. Study Area

The study area (34°40′–35°40′N, 99°0′–100°10′E) is located in the catchment of the Qushian River in the northeast of the QTP (Figure 1). The Qushian River is a tributary of the upper reaches of the Yellow River; it originates in the northern foothills of the Anyemaqen Mountains and flows into the Yellow River at Damitan Village. The altitude of the entire area ranges between 2000 and 5000 m. The upper reaches of the Qushian River are in mountainous areas with small intermountain basins, such as the Kuhai Lake basin and Maritan basin. The lower reaches of the river have developed small alluvial plains.

During the period from September to October 2009, a 30-day field investigation was conducted in the northern part of the catchment of the Qushian River. The field survey area is located between 35°15′–35°41′N latitude and 98°58′–99°43′E longitude, and its elevation ranges from 3562 to 5039 m, with an average altitude of more than 4000 m. The survey area has two mountains, named Erla Mountain and Jiangluling Mountain, and Kuhai Lake, which is a saltwater lake (Figure 1c).

The study area has a cool temperate continental climate. According to the monitoring of the Xinghai meteorological station (3535 m a.s.l) closest to the regional boundary (its location is marked in Figure 1b), the annual mean air temperature was 2.0 °C with a standard deviation of ±0.3 °C, and the annual precipitation was 200–370 mm during the period of 2003–2012. The flood season is from June to September, when the runoff accounts for about 70% of the total annual runoff. Precipitation in the flood season mostly occurs in the form of heavy rain or rainstorm, which often leads to flash floods in the mountain areas. Snow is the main form of precipitation in winter (from October to March), and the runoff generated in winter accounts for approximately 18% of the annual runoff. The vegetation types of the mountain areas are alpine meadow and swamp meadow, with the dominant plant being alpine Kobresia. Around Kuhai Lake at a relatively low altitude, there is an alpine steppe with Stipa purpurea as the dominant plant. The main soil type is silty loam, usually with gravels distributed on the surface.

2.2. Method and Data

2.2.1. GPR

The information on the permafrost boundary was obtained in three steps using GPR in this project.

(1)

Field survey and GPR data acquisition

Two methods were used to obtain the GPR data in this project: (1) the wide-angle reflection and refraction (WARR); and (2) the common-offset reflection (COR) method [30,31,41]. The WARR method is mainly used to detect the propagation velocity of electromagnetic waves and then determine the depth of the permafrost table, which is the key feature of GPR data interpretation. The COR method is used to detect the vertical and horizontal variations of a subsurface stratigraphic structure, especially to reflect the abnormal electromagnetic reflection signal due to the appearance or disappearance of permafrost in the horizontal direction as much as possible.

The equipment used for the field survey was a Professional Explorer (ProEx) GPR system (produced by Mala Corporation, Skolgatan, Sweden) with a rough terrain antenna (RTA) and unshielded antenna (UA). The central frequencies of the antennas are both 100 MHz. The RTA has the characteristics of a strong terrain coupling capability and high data acquisition efficiency and is especially suitable for mountainous environments, but it can only be used to perform COR survey tasks due to its fixed antenna offset. The UA has good anti-interference ability, and its transmitter and receiver can be separated, so it can perform both COR and WARR survey tasks. In the field investigation, we mainly used it to perform WARR tasks to determine the wave velocity at a specific location. When surveying with the RTA, we used a handheld GPS for positioning (Garmin Map60CS with a positioning accuracy of less than 15 m, produced by UniStrong Corporation, Beijing, China), and when working with the UA, a tape was used for the ground distance measurements. In the process of the survey, the change in surface conditions and their corresponding GPR track numbers needed to be recorded, especially for the COR profiles. Figure 2 shows the GPR profiles acquired with the UTA and UA, respectively. The same parameter settings were used for other profiles in this survey.

In the work, the layouts of the GPR profiles were designed according to the following principles: (1) these profiles should reflect the change of altitude; (2) they should cover different ASPs and cross different underlying surface types as far as possible. A total of 128 GPR profiles were deployed, most of which were longer than 500 m, and the longest profile reached ~3 km (

Table A1. Inventory of the GPR profiles and corresponding elevations of SPB.

ID of the GPR Profile	Start of the Survey Line		End of the Survey Line		Elevation of SPB (m)	ID of the GPR Profile	Start Of the Survey Line		End of the Survey Line		Elevation of SPB (m)
	Latitude (°N)	Longitude (°E)	Latitude (°N)	Longitude (°E)			Latitude (°N)	Longitude (°E)	Latitude (°N)	Longitude (°E)
P001	35.4856	99.5094	35.4854	99.5034	——	P065	35.4795	99.4232	35.4746	99.4268	4336
P002	35.4855	99.5023	35.4872	99.4954	4338	P066	35.4753	99.4279	35.4761	99.4295	——
P003	35.4852	99.5077	35.4851	99.5072	——	P067	35.4762	99.4295	35.4700	99.4297	4270
P004	35.4848	99.5057	35.4844	99.5056	——	P068	35.4690	99.4299	35.4696	99.4322	——
P005	35.3603	99.1728	35.3678	99.1688	——	P069	35.3459	99.2710	35.3459	99.2645	——
P006	35.3753	99.1704	35.3726	99.1725	4227	P070	35.3444	99.2769	35.3457	99.2717	——
P007	35.3659	99.1703	35.3662	99.1701	——	P071	35.3490	99.2790	35.3456	99.2754	4355
P008	35.3572	99.1450	25.3575	99.1449	——	P072	35.3462	99.2775	35.3468	99.2765	4354
P009	35.3583	99.1453	35.3552	99.1449	——	P073	35.2951	99.2537	35.2960	99.2476	4244
P010	35.3566	99.1449	35.3519	99.1684	——	P074	35.2667	99.2392	35.2677	99.2378	——
P011	35.3570	99.1561	35.3558	99.1556	——	P075	35.2684	99.2365	35.2711	99.2312	4217
P012	35.3569	99.1560	35.3567	99.1441	——	P076	35.3655	99.2561	35.3629	99.2495	——
P013	35.4743	99.4959	35.4731	99.4925	4262	P077	35.3261	99.2778	35.3308	99.2737	——
P014	35.4841	99.5071	35.4647	99.4915	4267	P078	35.3637	99.2867	35.3630	99.2860	——
P015	35.4647	99.4915	35.4656	99.4972	4218	P079	35.3630	99.2860	35.3635	99.2809	——
P016	35.4651	99.4956	35.4656	99.4974	4261	P080	35.3635	99.2809	35.3635	99.2768	——
P017	35.4583	99.4873	35.4569	99.4932	4205	P081	35.2503	99.2241	35.2538	99.2206	4257
P018	35.5012	99.4818	35.4783	99.4915	4346	P082	35.2558	99.2175	35.2613	99.2171	——
P019	35.4798	99.4899	35.4808	99.4914	4290	P083	35.2617	99.2195	35.2672	99.2159	4237
P020	35.5158	99.5099	35.5320	99.5075	4263	P084	35.2649	99.2299	35.2675	99.2278	4234
P021	35.5403	99.5074	35.5334	99.5182	4242	P085	35.2977	99.2553	35.3017	99.2463	——
P022	35.5369	99.5120	35.5379	99.5100	4228	P086	35.3460	99.1643	35.3423	99.1661	——
P023	35.5708	99.5268	35.5694	99.5312	——	P087	35.3452	99.1670	35.3475	99.1692	——
P024	35.5695	99.5308	35.5827	99.5345	4115	P088	35.3583	99.1448	35.3555	99.1453	4180
P024	35.5695	99.5308	35.5827	99.5345	4070	P089	35.3555	99.1459	35.3584	99.1461	4180
P025	35.5301	99.5025	35.5326	99.5030	4322	P090	35.3563	99.1570	35.3574	99.1526	4181
P026	35.5312	99.5019	35.5392	99.5017	4307	P091	35.3580	99.1346	35.3602	99.1543	4188
P027	35.6536	99.5281	35.6545	99.5450	——	P092	35.3585	99.1320	35.3611	99.1308	——
P028	35.6031	99.5177	35.6050	99.5314	——	P093	35.4077	99.1736	35.4030	99.1736	——
P029	35.6050	99.5320	35.6044	99.5479	——	P094	35.3977	99.1799	35.4001	99.1763	——
P030	35.5586	99.5052	35.5547	99.5170	4202	P095	35.3777	99.2784	35.3733	99.2794	——
P031	35.5540	99.5165	35.5525	99.5222	4151	P096	35.3692	99.2867	35.3732	99.2799	——
P032	35.5540	99.5218	35.5604	99.5201	4152	P097	35.3776	99.2891	35.3771	99.2853	4323
P033	35.4829	99.5002	35.4849	99.4982	4302	P098	35.3796	99.2875	35.3802	99.2840	4339
P034	35.4831	99.5001	35.4827	99.4994	4301	P099	35.3767	99.2856	35.3727	99.2793	——
P035	35.4922	99.4768	35.4876	99.4820	4392	P100	35.3784	99.2773	35.3770	99.2786	——
P036	35.4870	99.4818	35.4782	99.4901	4289	P101	35.3817	99.2994	35.3813	99.2964	——
P037	35.4087	99.5129	35.4039	99.5118	4275	P102	35.3864	99.2975	35.3816	99.2946	4370
P038	35.4039	99.5119	35.4054	99.5028	4255	P103	35.3684	99.2954	35.3731	99.2796	4295
P039	35.4054	99.5028	35.4095	99.5033	——	P104	35.3735	99.2880	35.3735	99.2837	——
P040	35.4098	99.5033	35.4110	99.5052	——	P105	35.3918	99.3080	35.3896	99.3072	——
P041	35.4007	99.5738	35.3990	99.5638	——	P106	35.4361	99.3883	35.4287	99.3813	——
P042	35.4093	99.5339	35.4079	99.5281	——	P107	35.4111	99.3436	35.4095	99.3472	——
P043	35.4078	99.5275	35.4063	99.5170	4305	P108	35.4119	99.3374	35.4094	99.3353	——
P044	35.4107	99.5036	35.4117	99.4978	——	P109	35.4063	99.3329	35.4078	99.3342	4228
P045	35.4798	99.4009	35.4820	99.4029	——	P110	35.4030	99.3328	35.4017	99.3378	——
P046	35.6368	99.4004	35.6345	99.3994	——	P111	35.4019	99.3323	35.4015	99.3373	——
P047	35.6327	99.3996	35.6255	99.3951	——	P112	35.3974	99.3438	35.3979	99.3433	——
P048	35.6256	99.3952	35.6197	99.3975	——	P113	35.3990	99.3267	35.3966	99.3282	4257
P049	35.6195	99.3972	35.6197	99.4065	4313	P114	35.4025	99.3103	35.3982	99.3165	4329
P050	35.6197	99.4088	35.6207	99.4154	4288	P115	35.4194	99.3708	35.4223	99.3723	4038
P051	35.5878	99.4262	35.5859	99.4200	——	P116	35.4069	99.3578	35.4084	99.3551	——
P052	35.5858	99.4199	35.5912	99.4247	4275	P117	35.4084	99.3551	35.4085	99.3540	4200
P053	35.5898	99.4267	35.5896	99.4296	4272	P118	35.4085	99.3539	35.4096	99.3502	——
P054	35.5896	99.4296	35.6009	99.4291	4288	P119	35.4045	99.3528	35.4080	99.3494	4159
P055	35.6097	99.4416	35.6143	99.4407	——	P120	35.4033	99.3482	35.4094	99.3504	4133
P056	35.6143	99.4403	35.6155	99.4396	4282	P121	35.3979	99.3433	35.3990	99.3422	——
P057	35.6104	99.4609	35.6070	99.4649	4159	P122	35.3990	99.3422	35.4005	99.3411	4199
P058	35.4660	99.4070	35.4644	99.4075	——	P123	35.3990	99.3267	35.3966	99.3282	——
P059	35.4645	99.4076	35.4636	99.4138	4318	P124	35.3938	99.3285	35.3957	99.3294	4251
P060	35.4635	99.4139	35.4633	99.4155	——	P125	35.3892	99.3371	35.3926	99.3324	4233
P061	35.4699	99.4252	35.4692	99.4282	——	P126	35.3957	99.3202	35.3958	99.3276	4252
P062	35.4683	99.4299	35.4644	99.4308	——	P127	35.3871	99.3096	35.3896	99.3078	——
P063	35.4637	99.4311	35.4632	99.4324	——	P128	35.3901	99.3102	35.3831	99.2995	——
P064	35.4767	99.4266	35.4794	99.4235	4330

). The altitude range of the GPR profiles is between 3900 m and 4700 m (Figure 3). The GPR survey was carried out from September to October of 2009, when the thickness of the active layer was close to the annual maximum, and the ground surface had not begun to freeze yet.

(2)

GPR data processing

In order to enhance deep signals and filter interference information on the GPR profiles, GPR data processing was necessary. This included the following steps: (1) subtract mean for the correction of signal saturation; (2) static correction for the adjustment of the time-zero position; (3) energy decay for the gain of signals; (4) background removal for the filtering of the horizontal signal; (5) band-pass filtering for the removal of specific frequency bands; (6) running average for the filtering of high-frequency noise signals; and (7) topographic correction. Among them, some are optional [30]. These steps are commonly used in GPR data processing for different targets, and the principles for their adoption are summarized in Neal’s report [31]. The processing was done using Reflexw software (Germany, introduced by http://www.sandmeier-geo.de/reflexw.html, accessed on 20 December 2021).

(3)

GPR data Interpretation

The interpretation of GPR data is the process of extracting permafrost information based on a variety of reference data. Firstly, the stratigraphic profiles from boreholes or pits that provide information on permafrost existence, soil texture, structure, etc. are the most important reference. Secondly, the change of the environmental factor in each profile, including the altitude, ASP, vegetation, landform, etc., is also considered. Google Earth, which provides a 3D visualization of remote sensing imagery, is a useful tool to aid in the interpretation of GPR data. Thirdly, the comparison and analogy of reflection features in different profiles are also the basis of interpretation.

The setting of the wave velocity follows the following principles: (1) the use of a wave velocity measured by WARR as mentioned above; (2) the use of a reverse-calculated wave velocity based on the depth of the permafrost table from a borehole or pit in or near the GPR profile; (3) the assignment of an empirical value derived from the wave velocity obtained by the above two methods according to the similarity of vegetation or micro-topography. Figure 4 and Figure 5 show several typical GPR profiles and their interpretation as examples, respectively, and Figure A1 gives more detailed information on these profiles and their display in Google Earth.

2.2.2. Boreholes and Pits

During the field investigation, 21 boreholes were deployed to detect permafrost and at 10 of which the ground temperatures were measured (~1 year after drilling) using thermistor temperature probes with an accuracy of ±0.05 °C (produced by the State Key Laboratory of Frozen Soil Engineering, Chinese Academy of Sciences). The rest of the boreholes were only used for the verification of the geophysical exploration, which helped to assess whether the permafrost existor not. At the same time, a number of pits were excavated, 39 of which were used as references for assessing the absence or presence of permafrost. In total, 60 ground truths from these boreholes and pits constitute a validation dataset. Among all these sites, 57 sites have definite records of vegetation types. In addition, we also collected soil samples from 13 pits and measured the soil volume moisture content by an oven-drying method in the laboratory. Then, the depth-weighted average moisture content within 1 m below the ground surface was calculated.

2.2.3. Spatial Data Products

The digital elevation model (DEM) used in this project was the ASTER GDEM V2 product with a spatial resolution of 30 m, which was produced by METI in Japan and NASA in the United States (downloaded from the Geospatial Data Cloud platform, http://www.gscloud.cn, accessed on 15 July 2021). The DEM data were used to calculate the topographic factors and estimate the potential incident solar radiation using ArcGIS software. For the analysis of the land surface temperature, MODIS LST products from 2003 to 2012, corrected by the method referred to in the literature [18], were adopted for the calculation of the multi-year average. The monthly air temperature data were extracted from the spatial dataset produced and corrected by Peng et al. [46] to calculate the multi-year mean air temperatures (downloaded from the Loess Plateau Science Data Center, National Earth System Science Data Sharing Infrastructure, National Science and Technology Infrastructure of China, http://loess.geodata.cn, accessed on 12 September 2021).

3. Results

3.1. Interpreted Results of GPR Profiles

The distribution of permafrost in mountainous areas is often fragmental and patchy due to the topographic impact (such as gullies formed by flowing water) and the complexity of the underlying surface. In the marginal areas of permafrost regions, the disappearance of permafrost is often abrupt; that is, permafrost disappears within a short horizontal distance. Some studies have shown that the depth of the permafrost table will increase considerably within a distance of less than 50 m near the edge of the permafrost region, and the frozen layer will quickly be pinched out [34,35], which generally occurs in the transition zone between continuous permafrost and seasonally frozen ground. When the GPR captures the horizontal variation in electromagnetic signals, it is possible to decipher information on the permafrost boundary from it.

GPR profiles generally pass through pits or boreholes that provide a reference basis for the interpretation of GPR data. In GPR images, strong and continuous in-phase reflection signals appear near the upper limit of permafrost (a depth range of 1.5–3.5 m in the study area, confirmed by pits or boreholes), often indicating the existence of permafrost. Thus, the main basis for assessing the boundary of permafrost patches is generally the interruption or disappearance of in-phase reflection signals that represent the permafrost table in the GPR images (Figure 2a and Figure 5a). In Section 2.2.1, the method of GPR profile interpretation is described in detail. Due to the uncertainty in the visual interpretation results of GPR, the extracted permafrost patch boundary is also called the suspected permafrost boundary (SPB). According to the GPS records during the field investigation using GPR, the geographic location and altitude of the permafrost patch boundary can be obtained. In total, 63 SPBs were identified and extracted from 128 GPR profiles (Table A1). For the rest of the profiles, some were entirely in the permafrost or seasonal frozen ground regions (e.g., the profiles in Figure 4), and the others were not easily interpreted due to a dry soil layer, excessive gravels, an insufficient detection depth of GPR, etc.

By analyzing the elevation of the SPBs, it was found that the most frequent occurrence of the SPB was between 4150 and 4350 m (Figure 6a), which indicates that this is the area where permafrost fragmentation and patches occur most frequently, as well as the transition zone from permafrost to seasonally frozen ground in the mountain permafrost region. The distribution of SPBs at different altitude zones is approximately normal. At the same time, the SPB also shows significant differences with different slope orientations. The statistical value of the south-facing slope is the largest, whereas the one of the north-facing slope is the smallest (Figure 6b). We plotted the lower limit of the permafrost along with the slope orientations in a polar coordinate system and found it can be regarded as a function of ASP (Figure 6c), which provides inspiration for improving the classical knowledge of permafrost distribution in mountainous permafrost.

3.2. Construction of an Empirical–Statistical Model of Permafrost Distribution

The slope’s facing has an impact on the thermal state of the ground by influencing the solar radiation, atmospheric convection, and heat conduction, which eventually affects the existence of permafrost on a local or larger scale. There have been several traditional understandings of the permafrost zoning in mountainous areas under the influence of ASP [5,37,47]. Among them, the permafrost zoning scheme based on the ASP that was proposed by King had a profound impact: the highest elevation without permafrost developing on the south-facing slope is defined as the lower limit of continuous permafrost, and the lowest elevation with permafrost existing on the north-facing slope is defined as the lower limit of discontinuous permafrost (Figure 7). The two boundaries divide mountain permafrost into continuous, discontinuous, and sporadic/seasonal frozen ground from high to low altitude, and the altitude of each lower limit was generally treated as a fixed value in a local region rather than as a function of ASP, possibly due to the difficulty of detection and lack of data. The distribution map of the frozen ground produced based on this principle may cause trouble for users, such as underestimating the area of continuous permafrost or seasonally frozen ground or overestimating the area of discontinuous permafrost.

According to the possibility of permafrost occurrence, the permafrost boundary or patch boundary can be detected by GPR mainly in the discontinuous permafrost belt. Thus, the closer the GPR profile’s location is to the upper continuous permafrost zone or to the lower seasonal frozen ground zone, the less likely it is to detect permafrost patch boundaries successfully, which is proved by the interpretation results of the GPR data (Figure 6a,c). Clearly, the possibility of the suspected permafrost patch boundary detected by GPR is affected by the ASP (Figure 6c), resulting in a new conceptual model of the mountain permafrost zonation presented (Figure 7).

In the new zonation scheme, the concept of “probable permafrost/possible permafrost/no permafrost” can be considered geographically equivalent to that of “continuous permafrost/discontinuous permafrost/sporadic permafrost and seasonal frozen ground” in King’s classical theory. The extent of the discontinuous permafrost zone becomes “narrow” and is regulated by the ASP, and the probabilities of the occurrence of permafrost and seasonally frozen ground, respectively, account for 50% in theory.

In this work, the layouts of the GPR profiles fully considered the influence of altitude and ASP, and relatively sufficient data were obtained (Figure 6a,c), providing the basis for building a statistical model. Based on the results from the GPR image interpretation, the relationship between the elevations of the permafrost patch boundary and the slope orientations can be described by a periodic function (Figure 8). The curve-fitting method was used to establish a mathematical model between the two indicators, and the model parameters were estimated. The form and parameters of the model are as follows:

$$y=a\sin \left(\frac{2\pi x}{360}+b\right)+c$$

(1)

where x is the slope orientation (degree), and y is the elevation of the SPB (m). The parameters obtained by curve fitting were: a = 91.7181, b = 4.8306, c = 4272.9235, R² = 0.5212, and p < 0.0001. The p value indicates that the result is significant.

By comparing the field investigation of the pits and boreholes, it was found that a 95% prediction interval is ideal for describing the possible permafrost zone, and its upper and lower limits are in good agreement with the ground truths (Figure 8b). The upper and lower limits of the prediction interval ($L_u$ and $L_l$) can be expressed by the following formula:

$$\{\begin{array}{c}{L}_u={\widehat{Y}}_0+t_{\alpha /2}\left(n-2\right)\sqrt{{\widehat{\sigma }}^2\left(1+\frac{1}{n}+\frac{{\left(x_0-\overline{x}\right)}^2}{\sum x_i^2}\right) }\\ L_l={\widehat{Y}}_0-t_{\alpha /2}\left(n-2\right)\sqrt{{\widehat{\sigma }}^2\left(1+\frac{1}{n}+\frac{{\left(x_0-\overline{x}\right)}^2}{\sum x_i^2} \right) }\end{array}$$

(2)

where ${\widehat{Y}}_0$ is an unbiased estimate of the conditional mean when $x=x_0$, n is the number of samples, $t_{\alpha /2}\left(n-2\right)$ is a critical value in the Student’s t distribution for $\left(n-2\right)$ degrees of freedom at a given confidence coefficient $\left(1-\alpha \right)$, ${\widehat{\sigma }}^2$ is the sample variance, $\overline{x }$ is the sample mean, and $x_i \left(i=1, 2, \dots ,n\right)$ is a sample of the population. Mathematically, a prediction interval is a range of values that is likely to contain the value of a single new observation given the specified settings of the predictors, and a detailed explanation of the prediction interval is given in the work by [48]. When the confidence interval is 95%, the value of α is 0.05, and there is a 95% probability that the predicted value will be in the interval.

Thus, the complete model can be described by the following formulas:

$$\{\begin{array}{c}P=1, H_0>L_u\\ P=0, L_l\le H_0\le L_u\\ P=-1, H_0<L_l\end{array}$$

(3)

where p = 1 represents probable permafrost, p = 0 represents possible permafrost, and p = −1 represents no permafrost. H0 is the actual altitude of the observation site. Figure 7 illustrates this empirical statistical model.

In this model, a 95% prediction interval indicates that the SPB has a 95% probability of falling within the prediction interval. In space, this area represents the transition zone from the permafrost to seasonally frozen ground, which corresponds to the discontinuous permafrost in King’s theory. Above the upper limit of the prediction interval, only a 5% probability is seasonally frozen soil theoretically, which is classified as probably permafrost, corresponding to continuous permafrost; below the lower limit of the prediction interval, only a 5% probability is permafrost, which is classified as no permafrost and corresponds to sporadic permafrost and seasonally frozen ground.

3.3. Model-Based Spatial Mapping and Evaluation

3.3.1. Frozen Ground Mapping by the Proposed Method

Based on the established empirical–statistical model, the spatial distribution of frozen ground in the study area was mapped using DEM and ASP data. According to the possibility of occurrence of permafrost patch boundaries, this map divides the frozen ground into three zones (probable permafrost zone, possible permafrost zone, and no permafrost zone) (Figure 9a).

3.3.2. Map Evaluation and Comparison with Two Existing Permafrost Maps

In order to evaluate the proposed new map (Figure 9a), a comparison was made with two existing maps. The first map was produced based on Nan’s model (referred to as Nan’s map). Nan et al. established a multiple regression model that only considers the altitude and latitude using limited ground temperature measurement data from boreholes located along the Qinghai–Tibet highway [21]. This model is generally considered to be one of the founders of the empirical–statistical model that later emerged to describe the distribution of permafrost in the Qinghai–Tibet Plateau. The expression of the model is as follows:

$$T_p=-0.83\phi -0.0049E+50.63341$$

(4)

where $T_p$ is the mean annual ground temperature near the depth of zero annual amplitude, $\phi$ is the latitude, and $E$ is the elevation. $T_p$ = 0.5 °C is the boundary to determine the existence of permafrost. This model was applied to map the permafrost distribution using the same DEM data as the proposed new map in this study (Figure 9b).

The second one is Zou’s permafrost map (referred to as Zou’s map), which was produced based on the MODIS land surface temperature and TTOP model. It is the latest permafrost distribution map of the Qinghai–Tibet plateau, with a spatial resolution of 1 km, and it was well verified by the field-measured data [18] (Figure 9c).

For the entire area, the three maps can accurately reflect the distribution of permafrost, although there are differences among them in detail. These differences occur mainly in small basins with relatively flat terrain, such as the Kuhai Lake basin and the Maritang basin. The field investigation showed that both permafrost (mean annual ground temperature range of −0.7 to −2.2 °C at ~4170 m) and non-permafrost (mean annual ground temperature of 0.03 °C at ~4200 m) areas exist at the Kuhai Lake basin. However, at the bottom of the Maritang basin, there is uncertainty about the existence of permafrost. Three shallow pits with a maximum depth of 1.5 m have been dug in this area, and no permafrost has been found. Neither Nan’s map nor Zou’s map reflects the observation facts above, but the map produced in this work can depict this well. Furthermore, on the slopes of the mountains, the possible permafrost zone is distributed around the probable permafrost zone in a skirt shape. Moreover, it can be reflected in detail that the distribution of the permafrost zone is affected by the ASP (Figure 9d–f). Therefore, the permafrost zoning map is consistent with the actual field survey results and theoretical analysis and has better rationality in describing the possibility of permafrost existence in mountainous areas.

However, most of the existing permafrost distribution maps with different spatial scales of the QTP, represented by the above two maps, only provide a binary classification of permafrost occurrence (with or without permafrost). The limited pit or borehole surveys also only provide binary information on the presence or absence of permafrost.

In order to evaluate the performance of the ternary classification map produced by this study, we proposed a method to calculate the agreement (consistency) between our ternary classification map and the binary maps or ground truths (

Table 1. The comparison scheme of evaluating consistency between our ternary mapping results and the existing binary maps/field survey dataset.

Different Zones	Abbreviation	Explanation	Abbreviation	Explanation	Calculation Method	Explanation
Probable permafrost zone	NPr	The total number of test points/pixels located in probable permafrost zone	NP	Number of test points/pixels with permafrost present in NPr	$A_{pr}=\frac{N_p}{N_{pr}}\times$100%	The consistency of probable permafrost zone ($A_{pr}$) can be expressed by the proportion of test points/pixels accurately identified as permafrost.
			Nnp	Number of test points/pixels with no permafrost in NPr
	SPr	The total area of probable permafrost zone	——	——	——	——
Possible permafrost zone	NPo	The total number of test points/pixels located in possible permafrost zone	NP	Number of test points/pixels with permafrost present in NPo	$A_{po}=\left(1-\frac{\left|\frac{1}{2}{N}_{po}-N_p\right|}{\frac{1}{2}{N}_{po}}\right)\times$ 100%	Ideally, permafrost and non-permafrost should each account for 50% of the possible permafrost zone. $A_{po}$ represents the degree to which the mapping results match the desired state.
			Nnp	Number of test points/pixels with no permafrost in NPo
	SPo	The total area of possible permafrost zone	——	——	——	——
No permafrost zone	Npf	The total number of test points/pixels located in no permafrost zone	NP	Number of test points/pixels with permafrost present in NPf	$A_{pf}=\frac{N_{np}}{N_{pf}}\times$ 100%	The consistency of the no permafrost zone ($A_{pf}$) can be expressed by the proportion of test points/pixels accurately identified as no permafrost.
			Nnp	Number of test points/pixels with no permafrost in NPf
	Spf	The total area of no permafrost zone	——	——	——	——
The entire region	St	The total area	——	——	$S_t=S_{pr}+S_{po}+S_{pf}$	——
	At	The total consistency	——	——	$A_t=A_{pr}\times \frac{S_{pr}}{S_t}+A_{po}\times \frac{S_{po}}{S_t}+A_{pf}\times \frac{S_{pf}}{S_t}$	$A_t$ is the overall mapping consistency calculated by the area weighted average method.

). By comparing the binary classification map and the ternary classification map, it was found that the possible permafrost type that corresponds to the discontinuous permafrost zone is the key to evaluating the performance of cartography. The consistency calculation is based on the assumption that the probability of both permafrost and non-permafrost occurrence is 50% in the possible permafrost zone in the new map of frozen ground. For the calculation of the consistency of the whole map, the area weighting method was adopted, and the proportions of different zones to the total area were taken as the weight of the spatial evaluation (Table 1).

Then, the new permafrost zonation map was compared with two existing frozen ground maps, and its agreements with the existing maps and field survey ground truths were analyzed, with consistency as an indicator (

Table 2. The areas and proportions of different permafrost zones based on the mapping results, as well as their consistency with existing maps and ground truth from survey field sites.

Frozen Ground Zone	Area (km2)	Area Percentage (%)	Ground Truth	Nan’s Map	Zou’s Map
Probable permafrost	2400	38.1%	87.5%	99.8%	86.5%
Possible permafrost	1575	25.0%	96.3%	91.6%	58.2%
No permafrost	2323	36.9%	82.4%	99.8%	92.9%
Total/Average	6298	100%	87.8% *	97.7% *	81.8% *

* represents the area-weighted average values.

). The coincidence degree between Nan’s map and the proposed permafrost zone map in this study was up to 97.7% (Table 2), whereas that between Zou’s map and the new map reached 81.8%. However, for areas that belong to the possible permafrost zone, the consistency between the two maps was only 58.2% (Table 2) because 70% of this zone is considered to be permafrost in Zou’s map, probably due to its lower resolution of 1 km. There are 60 pits or boreholes located in the field survey area (Figure 1), which provide evidence of the presence or absence of permafrost as ground truth (Figure 8b). They were also used to test the consistency between the permafrost zoning map and the real situation. The coincidence degrees between the three frozen ground zones and the ground truth reached 87.5%, 96.3%, and 82.4%, respectively. The weighted average of the entire region was 87.8% (Table 2). In general, the new permafrost zonation map performs well.

3.4. Temperature Characteristics at the Boundaries between Different Frozen Ground Zones

According to the above study, there are two invisible boundaries between the mountain permafrost sub-zones, which distinguish continuous permafrost zone, discontinuous permafrost zone, and sporadic and seasonal frozen ground zone. Approximately 1200 samples were selected from the two boundaries, and their multi-year average temperatures and ground temperatures during the period of 2003 to 2012 were calculated and are shown in boxplots in Figure 10. At the two boundaries, both the air temperature and land surface temperature have wide ranges of values and show the characteristics of approximate normal distribution. The lower limit of the discontinuous permafrost distribution (LLD) corresponds to the multi-year mean land surface temperature of 0.3 °C (standard deviation of ±1.0 °C) and the multi-year mean air temperature of −3.9 °C (standard deviation ±0.9 °C). The lower limit of the continuous permafrost (LLC) distribution corresponds to the multi-year mean land surface temperature of −1.3 °C (standard deviation of ±1.3 °C) and the multi-year mean air temperature of −5.7 °C (standard deviation of ±1.1 °C). King reported that the mean annual air temperature of −4 °C indicated the regional lower limit of the discontinuous permafrost zone in high-latitude mountains [5]. This is consistent with this study (−3.9 °C), although the air temperatures extracted from reanalysis data with a coarse grid have large uncertainties at a local scale [46].

3.5. Vegetation Types in Different Zones of Frozen Ground

The vegetation types of the field sites in the different frozen ground zones were analyzed (

Table 3. Statistics of field survey sites for different vegetation types and permafrost existence in different frozen ground zones. ASM, AM, and AS represent alpine swamp meadow, alpine meadow, and alpine steppe, respectively.

Frozen Ground Zone	Vegetation Type	Number of Samples	Number of Samples with Permafrost Present	Proportion of Samples with Permafrost Present	Notes
No permafrost zone	AS	8	3	37.5%	Although permafrost was found in only three sites with alpine steppe coverage, the three sites were all located in the seasonal wetlands around Kuhai Lake.
	AM	8	0	0%
	ASM	0	0	0%
	All types	16	3	18.8%
Possible permafrost zone	AS	6	1	16.7%	Permafrost was found in all sites with swamp meadows. The site with alpine steppe had the lowest possibility of permafrost.
	AM	11	3	27.3%
	ASM	3	3	100.0%
	All types	20	7	35.0%
Probable permafrost zone	AS	5	4	80.0%	The site with alpine steppe, where no permafrost was found, is located in the northeast of Kuhai Lake Basin.
	AM	13	12	92.3%
	ASM	3	3	100.0%
	All types	21	19	90.5%

). In the zone of no permafrost, most of the sites are covered by alpine steppe with relatively sparse vegetation, and in most sites where alpine meadow and alpine swamp meadow developed, permafrost was not found. The only exceptions were three sites around Kuhai Lake, where permafrost was found. These three sites are located on seasonal wetlands, the formation of which is related to the terrain around Kuhai Lake. All the sites with swamp meadow in the discontinuous permafrost zone have permafrost, and the sites with alpine steppe have the lowest possibility of permafrost developing. Overall, the possibility of permafrost occurrence in continuous permafrost or discontinuous permafrost, from high to low, is alpine swamp meadow (ASM) > alpine meadow (AM) > alpine steppe (AS).

In this project, special attention was paid to the discontinuous permafrost belt because the spatial variability of vegetation in this region may be more controlled by local hydro-thermal conditions rather than altitude and ASP. The vegetation type is generally a reflection of moisture conditions. The average soil water content data from a limited number of boreholes or pits located in the possible permafrost zone in the new map were extracted and analyzed. The results show that the soil water content of all sites with permafrost present is relatively high except for only one site, and the water content of the eight sites without permafrost is less than or equal to 25% (Figure 11). Based on the existing observations, it can be inferred that 25% may be an average soil moisture threshold determining the existence of permafrost, at least for most cases. It also partly explains why sites with good vegetation conditions tend to have a higher probability of permafrost occurrence.

4. Discussion

4.1. The Influence of Solar Radiation on Permafrost in Mountainous Regions

Altitude and solar radiation play an important role in the development and distribution of mountain permafrost [26,27,49,50], and solar radiation is largely regulated by the slope direction in mountainous areas [6].

Using the GIS platform, the annual total potential incident solar radiation on different ASPs and altitude zones were calculated and are shown in Figure 12a. In general, the value of the potential incident solar radiation increased as the altitude increased. At the same altitude zone, the potential incident solar radiation values of sunny slopes were significantly greater than those of shady slopes, and the maximum value appeared on the southwest-facing slope. Therefore, compared to the shady slopes, the lower limits of permafrost distribution are higher on the sunny slopes.

The ground temperatures measured from the boreholes in the field also revealed the influence of ASP on the thermal regime of permafrost. Figure 12b shows that the ground temperatures at a depth of 10 m on the sunny slope were higher than those on the shady slope by 1.4–1.6 °C at the same altitude. This difference between sunny and shady slopes was also revealed in other mountain areas. For example, the ground temperature difference between sunny and shady slopes in the Fenghuoshan Mountain in the hinterland of the QTP is 1.7–2.4 °C where abundant ground ice exists [51], whereas the differences reached 1.0–6.0 °C in the Tienshan Mountains, with higher latitudes and steeper slopes [52]. The reason for the small temperature difference between sunny and shady slopes in this area may be because the slopes where borehole sites are located are relatively gentle. In addition, the two boreholes (WQ01 and WQ02) located in the Kuhai Lake basin are special, and the ground temperature is 0.8–1.0 °C lower than that of the shady slope of the mountain region at the same altitude. Through the analysis of the surface conditions and core descriptions of the boreholes, it was determined that the two sites are located on seasonal wetlands with relatively flat terrain, and the existence of permafrost at these locations is mainly due to the influence of rich soil moisture content rather than ASP.

4.2. Significance and Limitation of this Model Based on GPR Data

The influence of ASP on permafrost can be verified and simulated using theoretical models [53], but it is difficult to observe directly and describe quantitatively. Some previous studies have shown that ground temperature can reflect the difference between shady slopes and sunny slopes to a certain extent [54]. However, there can still be great uncertainty in quantifying the impact of shady and sunny slopes from the perspective of ground temperature unless strict control conditions are adopted. Sometimes, periglacial geomorphic features on landscapes are used as alternative indicators to determine the lower limit of mountain permafrost, such as rock glaciers [55]. However, for areas with less steep terrain or insufficiently low temperatures, the typical periglacial phenomena may be very limited, such as the area of concern in this case.

This work used GPR as a field observation method to reveal the influence of ASP on the distribution of permafrost for the first time in a mountain region of the Qinghai–Tibet Plateau. The established zoning model of permafrost distribution in mountainous areas considering the adjustment of ASP is an improvement and supplement to King’s theory. However, it cannot distinguish between permafrost and no permafrost well, considering the characteristics of fragmentation and patches of permafrost in discontinuous permafrost belts and transient zones, where the permafrost development is affected by soil texture, soil moisture, vegetation cover, etc. comprehensively.

Although this model was developed in a local area, the law regarding the influence of ASP on permafrost distribution revealed that it can be referenced by other studies that involve mountain permafrost regions. In addition, the map of frozen ground, taking into account the ASP adjustment in this study, describes the distribution characteristics of mountain permafrost in detail, especially distinguishing the transition zone between permafrost and no permafrost. The permafrost in this zone is generally more sensitive to climate change and may degrade first under climate warming, bringing higher geological and engineering risks [26]. The permafrost mapping result of this work has a wide range of applicability in studying the differences in vegetation evolution and hydrological processes in different permafrost zones, as well as the occurrence of permafrost-related disasters.

GPR has a wide range of applications in the detection of sedimentary structures in permafrost regions, which mainly focus on the interpretation of vertical permafrost features [30,36,37,40,43,44,45]. When studying the spatial distribution of permafrost, GPR data can be regarded as a data source participating in statistical or machine learning models that are generally based on a large amount of data and support multivariate environmental data [22,23,24,25,32,49]. The participation of data with multiple scales and qualities will bring more uncertainty to the assessment of permafrost distribution and will also greatly increase the cost of resources and time. In this context, this project puts forward a new method of GPR application, which uses the horizontal abnormalities of electromagnetic signals recorded by GPR. It makes it possible to quickly build a distribution model of frozen ground relying on only GPR data and DEM. Obviously, this model is more efficient and easier to interpret.

However, a limitation is that the proposed permafrost mapping scheme has high requirements for the layout of the GPR profiles: (1) the GPR profiles need to reflect the variations in altitude and ASP as much as possible; (2) the GPR profiles should cross the possible boundaries of permafrost patches as much as possible, which are often marked by the transformation of the landscape; for example, the GPR profile can pass through from alpine meadow to alpine steppe; (3) a sufficient number of GPR profiles are necessary in order to obtain a statistical law. In order to guarantee the sufficiency of the survey, an empirical estimation is that at least 5–10 effective GPR profiles should be deployed on each slope’s facing (reclassified as east, south, west, and north).

5. Conclusions

In this project, GPR was used to survey the permafrost boundary in the mountainous area of the Qinghai–Tibet Plateau, and the interpretation results of the GPR profiles were used to establish a permafrost zoning model at a regional scale for the first time. It was proved that the GPR method has good applicability in the detection and mapping of permafrost in the mountainous areas with rugged terrain on the QTP.

The mountain permafrost zoning model, taking into account the ASP established by GPR, depicted the distribution of permafrost in the mountain area in detail and revealed that the area proportions of continuous permafrost, discontinuous permafrost, and seasonal permafrost in the region were 38.1%, 25.0%, and 36.9%, respectively. The LLC was 4472 m on the sunny slope and 4291 m on the shady slope, and the multi-year average land surface temperature and air temperature were −1.3 °C and −5.7 °C, respectively, near the boundary between the continuous permafrost zone and the discontinuous permafrost zone. Meanwhile, the LLD was 4258 m on the sunny slope and 4061 m on the shady slope, and the multi-year average land surface temperature and air temperature were −0.3 °C and −3.9 °C, respectively, near the boundary between the discontinuous permafrost zone and the no permafrost zone.

In mountainous regions, altitude leads to the vertical zonation of permafrost, and ASP regulates the distribution of permafrost by modulating the incoming solar radiation. The influence of ASP on the lower limit altitude of continuous and discontinuous permafrost is approximately 180–200 m. Thermal regime observations showed that the ground temperature on the sunny slope was 1.4–1.6 °C higher than that on the shady slope at the same altitude. However, in addition to the ASP, there are other local factors in this area. For example, the ground temperature of permafrost in the seasonal wetland near Kuhai Lake was 0.8–1.0 °C lower than that on the shady slope in mountain areas.

The elevation range of the discontinuous permafrost zone was 200–240 m on the vertical projection plane. The discontinuous permafrost zone is located on the outskirts of the continuous permafrost zone in the mountainous areas, but in the relatively flat areas of the intermountain basin, the permafrost distribution is characterized by patches and fragmentation. In the discontinuous permafrost zone, the leading factor determining the permafrost presence or absence may be soil moisture, which can be indicated by vegetation conditions to some extent. According to the field measurements of soil moisture from 13 pits, a 25% soil water content (the mean volume content within 1 m below the surface) can be used as a threshold to assess the presence or absence of permafrost in the discontinuous permafrost zone.