Mass livestock mortality events during severe winters, a phenomenon that Mongolians call

Mass livestock mortality induced by dry summers followed by unusually cold
and/or snowy winters, known as

Diagram showing

Understanding mechanisms and impacts of

Studies analyzing long-term variabilities in extreme climate conditions in
Mongolia are still limited because there are few long-term instrumental
records of climate in the region. The records that do exist are often not
continuous and contain missing data. Though historical documents record the
occurrence of

To improve risk analysis of

The objective of this study is to conduct risk analysis for the climatic
variables that cause

There are two important climatic variables to predict

In Mongolia, the term “

In order to estimate a return period of an extreme climate event, extreme
value theory (EVT) is useful (Cheng et al., 2014; Katz et al., 2002). There are ongoing debates about which methods are most suitable for estimating extremes, such as the return period and expected number of exceedances (Read and Vogel, 2015; Rootzén and Katz, 2013; Salas and Obeysekera, 2014). EVT informs us how to extrapolate a rare event which has not been experienced for a long time from existing observational data with a short record. EVT is a widely used method for estimating the probability of extreme hydroclimatic events (Katz, 2010; Leonard et al., 2014; Slater et al., 2021), such as floods (Prosdocimi et al., 2015; Willner et al., 2018), precipitation (Gao et al., 2018; Minářová et al., 2017), and compound events (Leonard et al., 2014). EVT helps us to formulate a risk management strategy by deriving a distribution of extreme climate events and estimating a possible extreme value for the future's preparedness. There are two main approaches in EVT: the block maximum approach and the threshold approach, which will be described in “Data and methodology”. The objectives of this study were to

estimate return periods of extreme drought conditions by using a reconstructed PDSI,

estimate return periods of extreme cold temperatures in Mongolia by using long-term instrumental data from Siberia.

We also explore the utility of using long-term climate proxies in the context of index insurance (Bell et al., 2013). In general, the index used for index insurance must be scientifically objective and easily measurable. The IBLIP in Mongolia uses the mortality rate as the index. Our study provides insights into the long-term variations in the mortality rate due to climate with the goal of reducing the bias and the variance of the estimates of the probability of the index used, by identifying the trend and using a longer record, respectively.

The PDSI is a standardized index that ranges from

Operational agencies, such as NOAA, use a range of

Spatial clusters of the mortality index based on 1972–2010

The correlation in PDSI values from 1700 to 2013 between three clusters is shown in Table 1. The Mann–Kendall trend test is used to examine the trends of the PDSI data (Kendall, 1948; Mann, 1945). The Mann–Kendall test shows that there are no monotonic trends in the PDSI data for all clusters (Table 1). Yet, time series of the tree-ring-reconstructed PDSI by clusters show that there is significant centennial-scale variability, which is important to consider since the time series suggest that there are persistent regimes that can last over decadal to centennial timescales (Fig. 3a–c). Though these may occur randomly or reflect systematic cyclical behavior, their consideration in a risk management strategy is critical.

Mann–Kendall trend test and correlation coefficients of PDSI values from 1700 to 2013 between the three clusters.

Time series of the tree-ring-reconstructed PDSI in

The autocorrelation function (ACF) and partial ACF of all the regions show that there are significant autocorrelations in the PDSI data in all clusters (in Figs. S1 and S2 in the Supplement). The development of a time series simulation model that uses these long lead correlations would help inform the risk analysis associated with the persistent regimes identified earlier. Autoregressive integrated moving average (ARIMA) models with different orders were evaluated based on the Bayesian information criterion (BIC), which can account for fitting errors for the Bayesian conditional mechanism of models. Please note that the BIC is a standard information-theoretic criterion whose relative magnitudes allow one to choose one model over another (Akaike, 1979; Burnham and Anderson, 2004). The order of the best ARIMA models in each cluster is (3, 0, 0) for the southwest, (1, 0, 2) for the northwest, and (1, 0, 0) for the east. These ARIMA models will be used later to forecast the effective return periods of droughts.

Models that use climate variables as covariates are explored for developing a nonstationary risk model. These data are summarized in Table 2. We use high-resolution gridded datasets of the Climate Research Unit (CRU) at the University of East Anglia for monthly temperature and summer (May–August) and winter (November–February) precipitation for the three clusters (Harris et al., 2014). All the gridded points within each cluster are averaged. We also used average monthly temperature data from instrumental records in Siberia, including Irkutsk (1882–2011), Minusinsk (1886–2011), and Ulan-Ude (1895–1989). We also use the Arctic Oscillation (AO) index (1903–2010), which comes from two sources: the Joint Institute for the Study of the Atmosphere and Ocean (JISAO) and the National Oceanic and Atmospheric Administration (NOAA) (Thompson and Wallace, 1998). The two records were merged into one record (e.g., Lall et al., 2016). The AO index is closely associated with summer and winter climates in East Asia (He et al., 2017). In particular, the negative phase of the AO is associated with more frequent cold-air outbreaks in East Asia, including Mongolia (Cohen et al., 2010; He et al., 2017; Yu et al., 2015). Finally, please note that although dry conditions of the PDSI are negative, all the analyzed PDSI values below are presented as reversed values (i.e., positive for dry conditions) because the R package, extRemes (Gilleland and Katz, 2016), will capture the maximum values.

Data analyzed in this study. WMO denotes World Meteorological Organization.

Extreme value analysis (EVA) is utilized in this study. In EVA, the
distribution of many variables can be stabilized so that their extreme
values asymptotically follow specific distribution functions (Coles et al., 2001). There are two primary ways to analyze extreme data. The first approach, the so-called block maxima approach, reduces the data by taking maxima of long-term block data, such as annual maxima (Coles et al., 2001). The generalized extreme value (GEV) distribution function is fitted to maxima of block data, as given by

Equation (1)

For mathematical notation,

GEV and GP distributions are fitted to the tree-ring-reconstructed PDSI values for approximately 300 years, from 1700 to 2013. Stationarity is assessed through the comparison of the BIC applied to a set of candidate models formulated using Eq. (5), with terms that include time or do not.

The procedure is implemented as follows:

Fit GEV distributions to the tree-ring-reconstructed PDSI values, allowing for nonstationarity by making

Fit GEV distributions to the tree-ring-reconstructed PDSI values using climate variables (AO index, summer precipitation, snow, and minimum temperatures).

Evaluate models based on the BIC.

Using the best GEV model, estimate return periods.

Repeat the above procedure for GPDs fitted to the tree-ring-reconstructed PDSI values.

The 95 % confidence intervals of parameters based on the normal approximation for each parameter. Also numerical values are listed in Table S1.

We construct two types of models: (1) stationary and nonstationary extreme value models and (2) nonstationary models using climatic variables as covariates. First, we consider polynomial models in time of the order of 0 to 2 for both the location and the scale parameters of the GEV distribution, resulting in seven models to be tested, including the stationary model, for each region. In addition, autoregressive (AR) models are examined. The models are evaluated based on the BIC (Table 3). The best GEV models and their maximum likelihood estimates (MLEs) with 95 % confidence intervals are as follows (Table 3, Fig. 4):

BIC values for stationary and nonstationary GEV models fitted to the tree-ring-reconstructed PDSI values.

Note that

These results suggest that in the long run, a stationary model for the PDSI in Mongolia may be appropriate. Only the southwest has nonstationarity in the scale parameter. This nonstationarity in the scale parameter for the southwest, with a mean coefficient of 0.002 relative to the constant value of 0.95, means that over 100 years the variability could increase from 0.9 to 1.05. If we take 0.9 to be a mid-period estimate, this would be rather a modest change. This could be a real feature or an artifact of the non-constant reconstruction variance from the tree-ring reconstruction algorithm.

The 95 % confidence intervals of parameters, using other climate variables based on the normal approximation. Also numerical values are listed in Table S2.

Next, we estimate parameters of the GEV distribution functions fitted to the
PDSI values by including other climate variables, such as the AO index, summer
precipitation, snow, and minimum temperatures, as covariates from 1903 to
2010. Summer precipitation is a mean of May to August of the previous year,
while snow is a mean of values from November of the previous year to the following February. Also, AO index data start in 1903. Thus, we use data starting in
1903 though the data themselves exist from 1901. The minimum temperature is a
minimum value from November of the previous year to the following October. The
GEV models with the lowest BIC for each cluster and MLEs with 95 %
confidence intervals are detailed below (Table 4 and Fig. 5).

BIC values in estimated GEV models fitted to the PDSI values using the climate variables from 1903 to 2010.

Note that bold BIC values mean the lowest values.

The time series of effective return periods of 100-year events for the GEV distribution functions fitted to the PDSI using the climate variables are shown in the southwest, northwest, and east from 1903 to 2010 (Fig. 6). This shows that variabilities in return periods of 100-year events of the PDSI values become larger over time in all the regions. Before 1940, the variabilities are small possibly because the instrumental data records began in the 1940s. Even after the 1940s, it also shows that the magnitude of 100-year events has increased in the last half of the data series. A PDSI value of 3 used to be a 100-year event in around 1920. Yet, at around the beginning of the 21st century, it had increased to be between 4 and 5. However, considerable inter-annual and decadal variability is evident.

Estimated effective return periods of a 100-year event from the GEV distribution function fitted to the PDSI values in the southwest over 1903 to 2010 with precipitation data as a linear covariate in the location parameter. Variabilities in return periods of 100-year events of the PDSI values become larger over time in all the regions. The horizontal blue line is the mean of the effective return periods, while the red one is its median. Please note that the vertical axis is shown by the reversed values of PDSI values, meaning that a positive value is a drought condition.

The relationship between significant climate covariates and reversed reconstructed PDSI values based on the best GEV models for each return period of 10-, 50-, and 100-year events is shown in Figs. 7 and 8. The figures show that less precipitation leads to higher reversed reconstructed PDSI values, meaning more likelihood of droughts. Consequently, with this model, future projections of precipitation could be helpful to predict drought severity and frequency.

Relationship between precipitation and reversed reconstructed PDSI values in the southwest

Relationship between precipitation, snow, and reversed reconstructed PDSI values in the northwest based on the best GEV model. Since the PDSI values are reversed, the positive values mean drought conditions. The

To fit a GPD, a threshold needs to be selected. We selected a threshold of 1.0 (please see Sect. S1 in the Supplement for a detailed explanation of how we chose the threshold). GPDs are fitted to the tree-ring-reconstructed PDSI values from 1700 CE as both stationary and nonstationary models (Table 5). The model of stationarity is best in terms of the BIC for all clusters.

BIC values for nonstationary models in the scale parameters of GPD models fitted to the tree-ring-reconstructed PDSI from 1700 for each cluster.

Note that bold BIC values mean the lowest values.

The likelihood ratio test shows similar results. The likelihood ratio between temporal linear and stationary models shows that the

Being similar to the GEV cases, we analyze the other climate variables after 1903. Table 6 shows that the best model of GPDs is the one with a constant in the scale parameters in terms of the BIC for all clusters. MLEs estimated by the best GPD models are shown in Fig. 9. The table shows that for catastrophic droughts, climate variables are not a significant covariate, although the differences in BIC values in the southwest and northwest between the ones with constants and with the AO index are small. The estimated effective return periods based on these best GPD models are listed in Table 7. In Table 7, the difference between the values for 10, 50, and 100 years is slight because the shape parameters estimated from the GEV for each case are negative. This means that the data are negatively skewed, and this leads to an implicit upper bound for the process. As a result, each of the quantiles is restricted by that upper bound, and they end up quite close to each other.

BIC values for different GPD models fitted to the tree-ring-reconstructed PDSI values from 1903 with climate variables for all clusters.

Note that bold BIC values mean the lowest values.

The 95 % confidence intervals of parameters, using other climate variables based on the normal approximation. Also numerical values are listed in Table S3.

Effective return periods of 10-, 50-, and 100-year events of the PDSI values, based on the best GPD models. (The actual PDSI values are negative ones of these values.)

In this section, we fitted the GEV distribution function and GPD function to the PDSI values. Results are the following:

The PDSI values will follow the distributions with

For the southwest, the nonstationary models performed better if we look at GEV models without a threshold. However, with a threshold of 1 for the GPDs, the stationary models perform better than the nonstationary models, which indicates that all trends in reconstructed PDSI values are influenced by small events and not by extreme events; i.e., extreme events are stationary. For both the northwest and the east, stationary models performed better for both the GEV and the GPD models.

Compared to the models with constants in the parameters, the GEV models with the climate variables are better in terms of the BIC value. Therefore, establishing a relationship between drought conditions and climate variables, particularly precipitation and snow, is useful in understanding the dynamics that determine dry conditions. However, compared to the models with constants in the scale parameters, the GPD models with the climate variables do not lead to improvement in the model performance in terms of the BIC.

In terms of the BIC, the models of a GPD fitted to tree-ring-reconstructed PDSI values show better performance than the GEV models.

Because of the third point, the effective return periods based on the GEV models change with the climate variables. In contrast, the effective return periods based on the GPD models are constant; for example, a 100-year event has the PDSI value of

Instrumental winter temperature data in Mongolia are limited before 1950. Also the gridded climate database that covers Mongolia starts after 1901. Thus, we attempt to estimate the Mongolia data from longer records from Siberia, which can go back to 1820. Existing studies suggest the winter temperatures between Mongolia and Siberia are correlated spatially, driven by polar jet dynamics (He et al., 2017; Iijima and Hori, 2018; Munkhjargal et al., 2020). First, winter temperatures in Mongolia will be simulated by using instrumental temperature data from Siberia (in Sect. 3.2). By using the simulated winter temperature in Mongolia, return periods of extreme cold temperature during winters will be estimated in Sect. 3.3.

The procedure was implemented as follows:

Conduct correlation analysis between Siberia and Mongolia data to select which station data are informative for temperature in Mongolia.

Impute missing data of instrumental data in Siberia.

Fit a GEV and GPD to the winter minimum temperature in Mongolia with the Siberia data.

Simulate the winter minimum temperature of Mongolia from Siberia data based on the best GEV model.

Calculate effective return periods of 10, 50, and 100 years from the simulated winter minimum temperature of Mongolia.

Next, we checked the structures of missing data from Irkutsk. Some years are
missing all monthly records. We impute Irkutsk's data with pattern-matching
methods, which are equivalent to

The results for GEV models based on the BIC are shown in Table 8. Models with Siberia data in both the location and the scale parameter have the lowest BIC for the northwest. For the southwest and east, the one with Siberia data in the location parameter and that is constant in the scale parameter shows the lowest BIC (Table 8). The best models for each region are shown in Fig. 10 and in the following:

BIC values for GEV models using Irkutsk data for three clusters.

Note that bold BIC values mean the lowest values.

The 95 % confidence intervals of estimated parameters based on the best GEV model fitted to the winter minimum temperature in three clusters using Irkutsk data. Numerical values are listed in Table S5.

For GPDs, we select 23

BIC values of GPD models using Irkutsk data for three clusters.

Note that bold BIC values mean the lowest values.

The 95 % confidence intervals of estimated parameters based on the best GPD model fitted to the winter minimum temperature in three clusters using Irkutsk data. Numerical values are listed in Table S6.

In this section, we fitted the GEV distribution and GPD to the winter minimum temperature in Mongolia. The results are as follows:

All the results show that the winter minimum temperature will follow the distributions with

Based on BIC, GPD models show better performance in both the southwest and the east regions, while the GED models show better performance in the northwest.

Next, we simulate the Mongolia winter minimum temperature based on data from
Irkutsk, Siberia, for 197 years using the parameters estimated by the best GEV
model. Then, using these simulated Mongolia winter minimum temperatures, we
estimate the 90% confidence intervals of return periods of 10-, 50-, and 100-year events for each cluster (Fig. 12). The medians of 100-year return periods are

Density plots of 10-, 50-, and 100-year return periods of the winter minimum temperatures in the southwest, northwest, and east of Mongolia with 90 % confidence intervals. Please note that the

Based on the thresholds used in the GPD approaches, we also explored if the
frequency of the co-occurrence of summer drought and cold winter temperatures has changed over time. First, we counted cases as a binary value of 1 when both summer drought and cold winter temperatures in Mongolia are below thresholds (

Binary index for the co-occurrence of threshold exceedance of PDSI values and winter temperature. The local regression is based on the optimal bandwidth of a local quadratic regression function based on the generalized cross-validation criteria considering that the binary indicator is an outcome of a nonhomogeneous Poisson process. Note the tendency for a cluster in the beginning for the northwest and the east. The increase in the frequency for the trend function in the most recent period could represent more of an edge effect of the regression.

Meteorological data in Mongolia are limited in length and have many missing
values. Therefore, we utilize longer records from paleoclimate proxy data and meteorological data from neighboring Siberia. The motivation was to improve risk estimation for

GEV models without a threshold show that there is a trend in tree-ring-reconstructed PDSI data in the southwest, while there is a no trend in the PDSI in both the northwest and the east. However, the threshold approach indicates that extreme events in reconstructed PDSI values are stationary, in turn indicating that catastrophic drought conditions have been stationary for the last 300 years.

The study estimated the extreme distributions of drought and winter minimum
temperatures in Mongolia. The PDSI values follow the distributions with

Based on the results of our GEV model fitted to the PDSI values, we show that climate variables, such as precipitation and snow, are important covariates for the extreme values of the reconstructed PDSI values. However, for catastrophic drought events, climate variables are not significant covariates based on the results of the GPD model fitted to the PDSI values.

The GEV model also shows that the return periods of drought conditions are
changing over time and variability is increasing for all the regions. Yet,
based on GPDs, the return periods of drought conditions are constant: for
example, the actual values of the PDSI for the 100-year events are

This study improves the return period estimation of droughts and winter minimum temperature. Summer drought and winter temperature are important predictors for livestock mortality since they explain 48.4 % of the total variability in the mortality data, along with summer precipitation and summer potential evapotranspiration (Rao et al., 2015). Therefore, this long-term estimation of return periods of these significant predictors can be used to improve risk analysis of high livestock mortality in order to prepare for the winter catastrophes through early warning systems and index insurance.

A binary index for the co-occurrence of threshold exceedance of drought
severity and temperature was developed and its temporal variation assessed. The index shows that all the regions have had increasing trends of this
co-occurrence since around 2000. Begzsuren et al. (2004) identify that mortality rates are higher in combined drought and

Our study estimates the return intervals and underlying probabilistic
characteristics of the climate variables. Index insurance requires a proper
threshold and the understanding of underlying distributions of risk events
(Haraguchi, 2018). Thus, the estimation of extreme value distributions
and return periods has the potential to improve livestock index insurance,
which is implemented in Mongolia by the government of Mongolia with the help
of the World Bank (Mahul et al., 2015). Insurance is priced by considering the uncertainty associated with the estimation of the probability of exceeding the threshold at which the payout occurs. The estimation of the uncertainty is reduced as the length of record (in our case from the paleoclimate extension) increases. At present, no one in the industry is using paleoclimatic information to extend and reduce coverage costs, but there is interest in using it to understand the clustering of payouts. Furthermore, the results of this study increase understanding of how extreme climatic events in arid regions, which are sensitive to anthropogenic climate change, are changing. Given that some research projects increases in droughts in Mongolia (e.g., Bell et al., 2013; Li et al., 2020), the urgent need to build resilience to winter disaster and

Codes are available upon request.

All climate-relevant data are publicly available, and data sources are clearly specified throughout the paper. All tree-ring data used in this paper are available from the International Tree-Ring Data Bank:

The supplement related to this article is available online at:

MH, ND, MW, and UL designed the research. MH conducted data analysis. MR and CL prepared the dataset. MH prepared the manuscript with contributions and feedback from all co-authors.

The contact author has declared that neither they nor their co-authors have any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “Understanding compound weather and climate events and related impacts (BG/ESD/HESS/NHESS inter-journal SI)”. It is not associated with a conference.

We thank Brian Dermody, the anonymous reviewer, and the editor for their invaluable comments, which helped to improve this paper immensely.

Nicole Davi and Mukund Palat Rao were supported by NSF OPP grant no. 1737788. Mukund Palat Rao was also supported by UCAR CPAESS NOAA Climate and Global Change Postdoctoral Fellowship under grant no. NA18NWS4620043B. Masataka Watanabe's work was supported by “Development of Innovative Green Technology and MRV Method for JCM (Joint Crediting Mechanism) in Mongolia”, which was funded by the Ministry of the Environment, Japan, from 2014–2020.

This paper was edited by Bart van den Hurk and reviewed by Brian Dermody and one anonymous referee.