Stochastic Weather Model Research Articles

Brief communication: SWM – stochastic weather model for precipitation-related hazard assessments using ERA5-Land data

Abstract. Long-term multi-hazard and risk assessments are produced by combining many hazard-model simulations, each using a slightly different set of inputs to cover the uncertainty space. While most input parameters for these models are relatively well constrained, atmospheric parameters remain problematic unless working on very short timescales (hours to days). Precipitation is a key trigger for many natural hazards including floods, landslides, and lahars. This work presents a stochastic weather model that takes openly available ERA5-Land data and produces long-term, spatially varying precipitation data that mimic the statistical dimensions of real data. This allows precipitation to be robustly included in hazard-model simulations. A working example is provided using 1981–2020 ERA5-Land data for the Rangitāiki–Tarawera catchment, Te Moana-a-Toi / Bay of Plenty, New Zealand.

A Stochastic Weather Model for Drought Derivatives in Arid Regions: A Case Study in Qatar

In this paper, we propose a stochastic weather model consisting of temperature, humidity, and precipitation, which is used to calculate a reconnaissance drought index (RDI) in Qatar. The temperature and humidity models include stochastic differential equations and utilize an adjusted Ornstein–Uhlenbeck (O–U) process. For the precipitation model, a first-order Markov chain is used to differentiate between wet and dry days and the precipitation amount on wet days is determined by a probability distribution. Five different probability distributions were statistically tested to obtain an appropriate precipitation amount. The evapotranspiration used in the RDI calculation incorporates crop coefficient values, depends on the growth stages of the crops, and provides a crop-specific and more realistic representation of the drought conditions. Five different evapotranspiration formulations were investigated in order to obtain the most accurate RDI values. The calculated RDI was used to assess the intensity of drought in Doha, Qatar, and could be used for the pricing of financial drought derivatives, a form of weather derivative. These derivatives could be used by agricultural producers to hedge against the economic effects of droughts.

Trivariate Stochastic Weather Model for Predicting Maize Yield

Maize yield prediction in the sub-Saharan region is imperative for mitigation of risks emanating from crop loss due to changes in climate. Temperature, rainfall amount, and reference evapotranspiration are major climatic factors affecting maize yield. They are not only interdependent but also have significantly changed due to climate change, which causes nonlinearity and nonstationarity in weather data. Hence, there exists a need for a stochastic process for predicting maize yield with higher precision. To solve the problem, this paper constructs a joint stochastic process that acquires joints effects of the three weather processes from joint a probability density function (pdf) constructed using copulas that maintain interdependence. Stochastic analyses are applied on the pdf and process to account for nonlinearity and nonstationarity, and also establish a corresponding stochastic differential equation (SDE) for maize yield. The trivariate stochastic process predicts maize yield with R 2 = 0.8389 and M A P E = 4.31 % under a deep learning framework. Its aggregated values predict maize yield with R 2 up to 0.9765 and M A P E = 1.94 % under common machine learning algorithms. Comparatively, the R 2 is 0.8829% and M A P E = 4.18 % , under the maize yield SDE. Thus, the joint stochastic process can be used to predict maize yield with higher precision.

SOME QUESTIONS OF ESTIMATING SUSPENDED SEDIMENT IN WATERCOURSES OF NORTH-WEST RUSSIA

In the practice of water management for economic purposes, calculations of suspended sediment for various time scales – from per-second to annual, are important. The estimation of annual suspended sediment transport, as well as of the statistical parameters of turbidity and the reliability of the estimates, is extremely difficult because of irregular and insufficient light conditions in different phases of the water regime. At the same time, owing to the knowledge of the processes that shape the quality of natural waters and a sufficient toolkit of calculation methods, the main indicators of water quality with can be reproduced with acceptable accuracy. The capabilities of statistical analysis of water quality indicators can be expanded by an integrated approach to estimating the indicators by means of well-proven deterministic and stochastic calculation algorithms with arguments observed regularly and for a long time. In this case, a composite method can be used to estimate the parameters of the suspended sediment distribution or water turbidity, which permits finding the parameters of the distribution curve of the function from the parameters of the distribution curve of its arguments. The paper presents a deterministic-stochastic modeling system “weather-runoff-suspended sediments”, based on a stochastic weather model, a model of runoff formation in a catchment area, and a model of annual suspended sediment transport. The system can estimate the distribution parameters of daily suspended sediment load and turbidity values in the situation of observed data shortage or changes in runoff formation in the catchment resulting from natural causes or economic activities.

A Bernoulli-Gamma hierarchical Bayesian model for daily rainfall forecasts

We consider stochastic weather models originally developed for rainfall simulations to build a hierarchical Bayesian mixture model for daily rainfall forecasts using endogenous and external information. We model daily rainfall as a seasonal-varying mixture of a Bernoulli distribution for rainfall occurrence and a gamma distribution for the rainfall amount. The model scheme allows the inclusion of predictors to reduce the bias and variance of the forecasts, while the hierarchical Bayesian framework promotes a better understanding and reduction in parameter uncertainties, especially for gauges with short records, as well as supports the estimation of regional parameters that could be employed for forecasts at ungauged sites. The model was tested using 47 years (1973–2019) of daily rainfall data from 60 gauges in South Korea. Climate indices derived from the low-level wind over the region were analyzed using Principal Component Analysis (PCA) and embodied into the model to enhance its forecast skills. The model structure was based on a detailed exploratory data analysis, which included the application of Self-Organizing Maps (SOM) to examine the spatio-temporal patterns of rainfall. Cross-validated results reveal improved skills over reference models based on climatology and persistence up to a three days lead time. The average gains in metrics such as the Brier and Winkler skill scores vary from 5% to 50%, while the average correlation skill between predictions and observations reach values up to 0.55. The gains beyond a three days lead time are marginal, but the underlying structure of the proposed model still encourages its use over the reference models, being a step forward in improving real-time daily rainfall forecasts for the region. It has also a great potential to be combined with weather model forecasts and applied in other places across the world.

Assessing marine operations with a Markov-switching autoregressive metocean model

This article presents a metocean modelling methodology using a Markov-switching autoregressive model to produce stochastic wind speed and wave height time series, for inclusion in marine risk planning software tools. By generating a large number of stochastic weather series that resemble the variability in key metocean parameters, probabilistic outcomes can be obtained to predict the occurrence of weather windows, delays and subsequent operational durations for specific tasks or offshore construction phases. To cope with the variation in the offshore weather conditions at each project, it is vital that a stochastic weather model is adaptable to seasonal and inter-monthly fluctuations at each site, generating realistic time series to support weather risk assessments. A model selection process is presented for both weather parameters across three locations, and a personnel transfer task is used to contextualise a realistic weather window analysis. Summarising plots demonstrate the validity of the presented methodology and that a small extension improves the adaptability of the approach for sites with strong correlations between wind speed and wave height. It is concluded that the overall methodology can produce suitable wind speed and wave time series for the assessment of marine operations, yet it is recommended that the methodology is applied to other sites and operations, to determine the method’s adaptability to a wide range of offshore locations.

Precipitation Regime Classification Based on Cloud-Top Temperature Time Series for Spatially-Varied Parameterization of Precipitation Models

Satellite and reanalysis precipitation products perform poorly over regions with low-density ground observation networks. In order to improve space-dependent parameterization of precipitation estimation models in data-scarce environments, the delineation boundaries of precipitation regimes should be accurately identified. Existing approaches to characterize precipitation regimes by seasonal or other climatological properties do not account for small scale spatial-temporal variability. Precipitation time series can be used to account for this small-scale variability in regime classification. Unfortunately, precipitation products with global coverage perform poorly at small time scales over data scarce regions. A methodology of using satellite-based cloud-top temperature (CTT) time series as a proxy of precipitation time series for precipitation regime classification was developed, and its potential and uncertainty were analyzed. A precipitation regime in this study was defined on the basis of characteristic small-scale temporal distribution and variability of precipitation at a given place. Dynamic time warping was used to calculate the distance between two time series. Criteria to select the optimal temporal scale of time series for clustering and the number of clusters were also developed. The method was validated over Germany and applied to Tanzania, characterized by complex climatology and low density ground observations. This approach was evaluated against precipitation regime classification based on a satellite precipitation product. Results show that CTT outcompetes satellite-based precipitation for classification of precipitation regime classification. The CTT-based classification can be used as precursor to spatially adapted precipitation estimation algorithms where parameters are calibrated by gauge data or other ground-based precipitation observations, and parameterization can be used for satellite-precipitation estimates, precipitation forecasts in numerical or stochastic weather models, etc.

A stochastic weather model for generating daily precipitation series at ungauged locations in the Catskill Mountain region of New York state

AbstractInformation on the variability of precipitation in time and space is critical for many water resource projects. However, precipitation records at the location of interest are often either limited or unavailable due to an inadequate network of rainfall measurements. To address this need, regionalization methods have been employed to characterize spatial patterns of precipitation and to transfer precipitation information from one location to another where records are scarce. Hence, the overall objective of the present paper is to propose a stochastic weather model for generating daily precipitation at ungauged locations. The proposed approach consists of two components: (a) a regionalization approach for identifying homogeneous groups of observed daily precipitation series, and (b) a stochastic model for constructing daily precipitation events at ungauged locations within homogeneous groups. This statistical approach identifies groups of precipitation stations with similar statistical characteristics based on the combination of two multivariate statistical techniques: principal component analysis (PCA) and ordinal factor analysis (OFA). While the application of PCA in climatological regionalization studies based on precipitation amount is common, the application of OFA to include precipitation occurrence in the identification of regions is unusual. The feasibility of the approach is assessed using daily precipitation data from a network of precipitation stations in the Catskill Mountain region of New York State, United States.

Stochastic weather and climate models

Although the partial differential equations that describe the physical climate system are deterministic, there is an important reason why the computational representations of these equations should be stochastic: such representations better respect the scaling symmetries of these underlying differential equations, as described in this Perspective. This Perspective also surveys the ways in which introducing stochasticity into the parameterized representations of subgrid processes in comprehensive weather and climate models has improved the skill of forecasts and has reduced systematic model error, notably in simulating persistent flow anomalies. The pertinence of stochasticity is also discussed in the context of the question of how many bits of useful information are contained in the numerical representations of variables, a question that is critical for the design of next-generation climate models. The accuracy of fluid simulation may be further increased if future-generation supercomputer hardware becomes partially stochastic. Although the differential equations that describe the physical climate system are deterministic, there are reasons, both theoretical and practical, why computational representations of these equations should be stochastic. This Perspective surveys the benefits of stochastic modelling of weather and climate.

Detectability of historical trends in station‐based precipitation characteristics over the continental United States

AbstractThe goal of this paper is to detect secular trends in observed, station‐based precipitation variations and extreme event occurrences over the United States. By definition, detectable trends are those that are unlikely to have arisen from internal variability alone. To represent this internal variability, we use station‐specific, seasonally varying, daily time scale stationary stochastic weather models—models in which the simulated interannual‐to‐multidecadal precipitation variance is purely the result of the random evolution of daily precipitation events within a given time period—to first estimate the trends in various means and extremes that can occur even with fixed, climatological daily precipitation characteristics. Detection of secular trends in the observed climate—whether naturally or anthropogenically induced—can then be defined relative to this stochastic variability, i.e., as trends in the means and/or extremes that are likely to have occurred only through a change in the underlying precipitation characteristics. The derived results have two important ramifications. First, they identify “hot spot” regions in which trends in precipitation characteristics are already emerging from within the envelope of stochastic variability, including (but not limited to) positive trends in annual occurrence across most of the U.S. and positive trends in annual intensity and heavy‐event accumulations across the Interior Plains and around the Great Lakes. Further, they identify “sentinel” metrics which show the greatest detectability—e.g., annual precipitation occurrence and intensity—as well as those which show the least detectability and hence are unlikely to produce any statistically meaningful signals—e.g., seasonal total precipitation and extremes.

Characterizing the Potential Predictability of Seasonal, Station-Based Heavy Precipitation Accumulations and Extreme Dry Spell Durations*

Abstract The release of seasonal (and longer) predictions of various climatological quantities is now routine. While undoubtedly devastating to lives and livelihoods, it is unclear whether seasonal extremes in precipitation—for example, extreme dry spells leading to droughts or heavy precipitation events leading to flooding—represent a feasible target for these predictions, that is, whether they are potentially predictable or are instead inherently unpredictable more than a few days to weeks in advance. This paper assesses the potential for predicting seasonal extremes in observed precipitation as a function of region and time of year by decomposing the station-based variance into that attributable to short-memory behavior of typical meteorological events—as generated from station-specific, seasonally varying, daily time-scale stationary stochastic weather models (SSWMs)—and that attributable to longer-time-scale, potentially predictable changes in precipitation-producing processes. Findings suggest the potential for making skillful predictions of seasonal precipitation extremes over the United States is enhanced (reduced) during the cool (warm) season, particularly for heavy precipitation event accumulations. Further, this potential is accentuated along the West Coast, around the Great Lakes, and over the central plains and Ohio River valley but is diminished over the Northeast and northern Great Plains. However, findings also suggest the potential for producing seasonal (and longer) predictions of seasonal precipitation extremes is spatially and seasonally dependent. As such, this paper includes supplemental material for the potentially predictable variance of seasonal extreme dry spell lengths, heavy event accumulations, and total accumulations at 774 stations across all 365 days so readers can evaluate the potential predictability for the location, timing, and metric of most relevance to them.

The Potential Predictability of Precipitation Occurrence, Intensity, and Seasonal Totals over the Continental United States*

Abstract Using weather station data, the parameters of a stationary stochastic weather model (SSWM) for daily precipitation over the contiguous United States are estimated. By construct, the model exactly captures the variance component of seasonal precipitation characteristics (intensity, occurrence, and total amount) arising from high-frequency variance. By comparing the variance of the lower-frequency accumulations (on the order of months) between the SSWM and the original measurements, potential predictability (PP) is estimated. Decomposing the variability into contributions from occurrence and intensity allows one to establish two contributing sources of total PP. Aggregated occurrence is found to have higher PP than either intensity or the seasonal total precipitation, and occurrence and intensity are found to interfere destructively when convolved into seasonal totals. It is recommended that efforts aimed at forecasting seasonal precipitation or attributing climate variability to particular processes should analyze occurrence and intensity separately to maximize signal-to-noise ratios. Significant geographical and seasonal variations exist in all PP components.

The stochastic weather model in the system of deterministic and stochastic modeling of runoff and nutrient load

The estimation is carried out of the distribution functions of annual runoff and nutrient load on the Russian part of the Gulf of Finland (the Baltic Sea) formed by different pollution sources. The stochastic weather model is used for the estimation.

Basin-Scale Water Resources Assessment in Oklahoma under Synthetic Climate Change Scenarios Using a Fully Distributed Hydrologic Model

Climate change resulting from the enhanced greenhouse effect is expected to have significant implications for the hydrological cycle. Several studies have pointed out the importance of basin-scale investigations for determining regional impacts on water resources, including the effects of floods and droughts. In this study, a fully distributed hydrologic model is used to assess the potential impacts of climate change on water availability in a basin in Oklahoma (United States). With this aim, the hydrologic model was applied for current conditions as well as under the hypotheses of climate variations represented by scenarios consistent with a climatic trend analysis generated using a stochastic weather model. Hydrologic simulations indicate that streamflow and evapotranspiration reflect variations in precipitation differently. Positive trends in precipitation result in an increase in surface and groundwater resources, while evapotranspiration is only affected slightly due to the higher soil moisture in the basin. Sensitivity analyses of the evapotranspiration and runoff changes to precipitation variations confirm these results. Comparisons of the impacts of the precipitation trend on surface and groundwater resources showed that the increase of surface water resources is ∼3 times greater, implying the groundwater system is affected less by climate change. The use of a distributed model also provided insight on the spatial variation of the water balance components. Results showed that the most significant increases of soil moisture (∼60%) are located along the river network and in the flat areas of the basin, characterized by a higher frequency of saturation excess runoff. In summary, climate change scenarios in this region produced an increase in water resources that can have beneficial impacts, but these positive effects are tempered by the increasing potential for flood risk. The increase of this risk has been evaluated as well in this analysis.

Automated Generation of Reduced Stochastic Weather Models I: Simultaneous Dimension and Model Reduction for Time Series Analysis

We present a method for simultaneous dimension reduction, model fitting, and metastability analysis of high-dimensional time series. The approach is based on the combination of hidden Markov models (HMMs) with localized principal component analysis (PCA) (which is used to identify the essential dimensions in the form of empirical orthogonal functions (EOFs) for each of the hidden states) and fitting of multidimensional stochastic differential equations (SDEs). This means that the analyzed data is clustered according to differences in essential dimensions and SDE models specific to each of the hidden states. We derive explicit estimators for PCA-SDE model parameters in the case of fixed sequences of HMM states and employ the expectation-maximization algorithm for numerical optimization of HMM-PCA-SDE parameters. We demonstrate the performance of the method by application to historical temperature data in Europe during 1976–2002. In a comparison with the standard SARMA (seasonal autoregressive moving average model) technique for time series analysis, the HMM-PCA-SDE method exhibits better numerical performance and efficiency, especially on high-dimensional data sets and for a 20-dimensional reduced state space. We also compare the results of both models w.r.t. errors of one-day temperature predictions.

Developing daily precipitation scenarios for climate change impact studies in the Guadiana and the Tejo basins

Abstract. Hydrological models to evaluate the impacts of climate change in the water resources sector require spatially correlated daily precipitation scenarios as model inputs. This paper presents a practical procedure for developing such precipitation scenarios using multisite stochastic weather models or generators conditional on large-scale daily circulation patterns, based on GCM-simulated future mean sea level pressure (MSLP) fields. The procedure is demonstrated on the basis of HadCM3 and HadAM3H simulations with an example for two river basins in the Iberian Peninsula. Changes in daily precipitation scenarios for the region generated by stochastic models are consistent with large-scale precipitation scenarios from direct GCM outputs; however, more localised characteristics have to be found from downscaled precipitation scenarios rather than from direct GCM outputs. This may imply that possible changes in downscaled precipitation reflect the underlying physics in GCMs, so that downscaled daily precipitation scenarios may be more suitable for impact models than the coarse GCM outputs.

天候デリバティブの価格付けへ向けた日次降水量の確率モデル化

Weather derivatives are getting to be powerful tools for weather risk hedging. A popular method which draws out valid prices of weather derivatives is a stochastic modeling approach. In the method, expected payoffs of weather derivatives based on stochastic weather models are regarded as their valid prices. Although useful stochastic models of temperature have been shown, stochastic models of daily rainfall are still being developed. Therefore, it is considered that pricing of daily rainfall derivatives is difficult. This paper shows a new stochastic daily rainfall model for pricing daily rainfall options. The new model in which a modified geometric distribution model is applied can express stochastic features of daily rainfall. Furthermore, this paper also shows that the combination model of the Markov chain rainy day model and the new model can express stochastic features and risks of daily rainfall option payoffs.

Weather data generator to study climate change on buildings

Most computer programs that analyse the yearly performance of buildings require an input of historical series of weather data measured at the location of interest. However, analyses of climate change scenarios needs hourly weather data series that allow realistic changes in various weather parameters. This can not be done easily with the reference years based on measured weather data normally used. In this paper a weather generator is proposed in which climate changes can be implemented. Based on weather data observed over years a stochastic weather model is developed. This model is used to make a general model independent of the location and with which climate changes can be simulated. The general model can be adapted to a local climate change. Only new averaged values of the weather variables being the result of a climate change should be used as input. The model is able to generate hourly weather data that can be used as input for all kind of simulation programs to study the effect of climate change on the design and energy consumption of HVAC systems.

Multisite stochastic weather models for impact studies

AbstractStochastic weather models have been developed for simultaneous simulations of daily precipitation, and daily maximum and minimum temperatures at multiple sites in a river basin in order to reproduce the interstation correlations and self‐consistency in weather series. The basic structure of the stochastic weather models was adopted from Wilks (1999. Agricultural and Forest Meteorology 96: 85–101), but an extension was made to condition the model parameters on daily circulation patterns. Model parameters were also estimated without conditioning on daily circulation patterns, so that both conditional and unconditional simulations were conducted and compared. Statistical analyses on the synthetic weather data imply a better performance of the conditional simulations, on most aspects of the required statistics. In addition, the conditional weather models on daily circulation patterns can be applied directly in impact studies, for the purpose of downscaling climate scenarios from climate model simulations, and some related aspects are also discussed. Copyright © 2002 Royal Meteorological Society.

Thermal behaviour of a heated building under random weather condition in Warsaw

The paper discusses thermal analysis methodology applied to buildings, in which the stochastic nature of the external and internal forces is concerned. The forces are as follows: ambient temperature, solar radiation and heating or cooling load. The principle of superposition is applied to the deterministic and the random components for the concerned weather parameters as well as the state variables. The weather model, which has been constructed, is indispensable in determining the thermal behaviour of a building stochastically. The stochastic weather model expresses the joined and mutual influence of the external temperature and solar radiation on the building's thermal performance. This stochastic approach, presented in the paper, to a simple example is applied, just for the verification purposes. Computer simulations of a heat loss process for a simple two-node dynamic model of a heated building have been carried out. The heating system is either controlled or works without that device. At first, heating installation has been working either constantly or intermittently. As a result of numerical computation, the distribution of mean indoor temperature and heating load has been obtained, as well as their standard deviations. But in order to evaluate the influence of solar direct gains on a room's heat balance the same computer simulations have been carried out for the single forcing function—the external temperature. Moreover, to underline the effect of solar radiation on the room's temperature the heating installation has been turned off and the inner temperature is settled only as the result of weather condition. With regard to those simulations—time history of mean room temperature as well as its standard deviations has been computed. The identification procedure of the weather parameters has been based on a 10-year meteorological data for Warsaw.