Glacier melt is strongly impacted by climate and meteorology. Temperature lapse rates are used to model glacier melt, and the accuracy of the spatial distribution of modelled melt can be impacted by the lapse rate used in modelling. Additionally, the observed spatial distribution of melt is highly temporally variable. Whether this variability is caused by lapse rate is unknown. Storglaciären and Rabots glaciär in Northern Sweden were equipped with temperature measurement stations at both low and high glacier elevations over the 2014 ablation season. From these measurements, surface lapse rates 0.1 m above the glacier surface, and near-­surface lapse rates 2 m above the surface, were calculated for the two glaciers. The lapse rates were then compared to meteorological variables measured in the middle of the glaciers’ elevation range. In addition, a comparison was made with ablation data collected via ablation stakes throughout the melt season. On both Storglaciären and Rabots glaciär, the surface lapse rate is −0.28 °C (100m)−1 averaged over the ablation season. The season ­average near­-surface lapse rate is also the same for both glaciers, at −0.37 °C (100m)−1. The lapse rate values are shallow in comparison to non-­glaciated mountain areas. The meteorological variables of wind speed and precipitation affect surface lapse rate on short timescales. Long-­term patterns in surface lapse rate are influenced by incoming radiation, humidity and precipitation. In addition, topographic shading and albedo impact the incoming short­-wave radiation, causing diurnal and seasonal fluctuations in surface lapse rate. A cumulative approach to lapse rate using a positive degree day gradient reflects the pattern of ablation gradients measured through the ablation season. However, a lack of data means no robust conclusions can be drawn from this comparison. Many melt modelling studies use steeper lapse rates in ablation and mass balance modelling than observed over Storglaciären and Rabots glaciär. This can lead to underestimation of ablation at high glacier elevations. Measurements of local lapse rates recorded over glacier surfaces are necessary in order to produce more accurate ablation modelling results.

This work deals with the topic of lapse rate modelling in the field of Life Insurance. First, the theoretical apparatus is established: the linear models and their extension, generalized linear models. Furthermore, we describe the process of model selection and evaluation. In the second part of this work we describe the influence of various individual as well as macroeconomical parameters on the lapse rate. We summarize the findings of previous works in this field. The last part introduces models in statistical software R based on generalized linear models and describes the process of their selection and evaluation. Outputs from these models are interpreted and compared to the ratio analysis results.

1970 至 1980 年代初期，美國壽險業在高市場利率的衝擊下，壽險保單持有人為尋求更高的投資報酬，紛紛提出解約(Lapse)或保單貸款(Policy loans)的要求，產生所謂的脫離金融機構症(Disintermediation)，此現象可能造成保險公司現金大量流出，進而影響公司的資金運用。故美國壽險公司為降低此種利率不正常變動所造成之影響，便致力開發變額壽險等與利率相關的保單商品。 人壽保險契約解約率(Lapse rate)過高一直是壽險公司經營上的困擾，解約率的高低除直接反應保單的穩定性外，亦可作為公司業務成長及業務品質的重要指標。我國對於影響壽險契約解約率因素的研究多以問卷調查的方式為之，藉此瞭解個別保戶解約的動機，屬個體面的探討，此種研究方法可能無法直接反映總體經濟環境的改變所造成的影響。由歐美國家學者提出的相關研究，顯示其已漸漸重視總體經濟環境興壽險解約率間的相互關係。反觀國內並無相關的研究文獻，故本論文即以壽險解約率與總體經濟關係為研究的主題。 本論文的實證研究受限於國內壽險業發展較晚及資料取得不易，故以成立時間較久的七家本土壽險公司為研究樣本，以民國 72 年至 85 年為研究期間，被解釋變數則分為保額解約率及件數解約率兩項，解釋變數為經濟成長率、平均每人國民所得、替代資產報酬率、失業率及通貨膨脹率。並以橫斷面及時間序列結合資料(Panel data)型態應用於壽險解約率的模型建構，此資料型態可解決壽險解約率相關資料太少，無法有足夠樣本建構橫斷面或時間序列資料型態的模型，故本研究採用此種資料探討壽險保單解約率與總體經濟變數間的關係，並透過各種檢定方法，選取解約率模型。 實證結果顯示國內經濟成長率及平均每人國民所得對壽險保額解約率及件數解約率皆有顯著的影響，失業率在轉換前的件數解約率模型為顯著，替代資產報酬率及通貨膨脹率皆不顯著。此實證結果可能因變數選取的不適當而扭曲，但壽險公司仍可根據本研究的研究方法，修正有關的解釋變數建立適合公司的解約率模型，提供壽險公司擬定相關策略，降低總體經濟變動對壽險公司解約率的衝擊。 / Lapse rate plays a crucial role in monitoring the effectiveness of management for life insurers. Its changing phoneme not only characterizes the stability of the insurer's financial strength but also provides a benchmark in valuing the development and quality of business. There are many factors influencing the lapse rate of the life insurance policies. In this study, macroeconomics index, economic growth rate, per capita income, rate of return on alternative, unemployment rate and inflation rate are selected as independent variables to measure their importance. Seven Taiwan domestic life insurers between 1983 and 1996 are sampled and studied. The panel data approach combining cross sectional and longitudinal observations are adopted. The lapse rate of the insured amount and the insured case are selected in variable intercept regression model as dependent variable to summarize the mutual relationship with the chosen independent variables. F-tests, Lagrangian-multiplier test and Hausman test are performed in making the conclusion. Based on our study, several results have been found and summarized as following. (1) Economic growth rate and per capita income are found to be significant in influencing both the lapse rates of insured amount and insurance case. (2) Unemployment rate is also significant in influencing the lapse rate of insurance case. (3) There is no significant effect from the rate of return on alternative and inflation rate. This study has emphasized on employing the methodology of adopting the panel data to explore the relationship between the lapse rate and the selected macroeconomics factors. Based on our approach, the life insurers could monitor its renewal life insurance policies and associated cash flows when the impacts from the macroeconomic factors present.

Thesis (MScEng)--Stellenbosch University, 2011. / ENGLISH ABSTRACT: The meteorological conditions at Eskom’s Majuba Power Station are measured, evaluated and trended in this dissertation. The results are used to evaluate the current natural draught wet-cooling tower (NDWCT) design- and performance test specifications and to compare these to the original design- and performance test specifications. The evaluation reveals that the design parameters for the NDWCTs at Majuba Power Station, a cooling system that was originally designed optimally, could have been determined differently and arguably more accurately by using the wet-bulb temperature (Tawb) as the main design variable instead of the dry-bulb temperature (Ta). A new technique to determine optimal NDWCT design and performance test conditions is consequently proposed. In order to satisfy the atmospheric conditions required for a successful NDWCT performance test, it is also proposed that the tests be undertaken between 12:00 and 14:00 during Summer. It is found that the NDWCT inlet Tawb, measured at specific heights, does not compare well to the far-field Tawb measured at the same heights when a Tawb accuracy of 0.1 K is required. It is proposed that a more representative far-field Tawb measuring height of 10 m should be used in future NDWCT designs as the NDWCT design temperature reference height. The industry-standard reference height should, however, still be used during temperature profile calculations. A parametric study of the water-steam cycle and wet-cooling system at Majuba indicates that during full load conditions, the generated output (Pst) is primarily dependent on the condenser saturation pressure (pc). The latter is reliant on Tawb, the temperature lapse rate (LRT) that is represented by the temperature profile exponent (bT), the main cooling water flow rate (mcw), atmospheric pressure (pa), and wind speed (VW). Using historical plant data relatively simple methods, enabling the quick and effective determination of these relationships, are proposed. The plant-specific and atmospheric parameters required for these analyses are also tabulated. Two NDWCT effectiveness models, one mathematical (Kröger, 1998) and one statistical artificial neural network (ANN) model are presented and evaluated. ANNs, which are not often used to evaluate NDWCT effectiveness, provide accurate NDWCT temperature approach results within 0.5 K of measured values for varying dependent variables. This motivates that an ANN, if set up and used correctly, can be an effective condition-monitoring tool and can be used to improve the accuracy of more empirical NDWCT performance models. The one-dimensional mathematical effectiveness model provides accurate results under NDWCT design conditions. The dependency of Majuba’s NDWCT to the rain zone mean drop diameter (dd) is evaluated by means of the one-dimensional mathematical model. A reduction in dd from 0.0052 m to 0.0029 m can reduce the NDWCT re-cooled water temperature (Tcwo) so that the rated pc is reduced by 0.15 kPa, which relates to a combined financial saving during peak and off-peak periods of R1.576M in 2013 and R1.851M in 2016. Similar improvements can result in higher savings at other wet-cooled stations in the Eskom fleet due to less optimally-designed wet-cooling systems. The proposed techniques should be considered in future economic evaluations of wet-cooling system improvements at different power stations. / AFRIKAANSE OPSOMMING: Die meteorologiese toestande by Eskom se Majuba-kragstasie is deur die navorser gemeet en -evalueer. Die resultate word gebruik om die Natuurlike-trek, Nat koeltoring (NTNKT) se ontwerp- en werkverrigting toetsspesifikasies te evalueer en vergelyk met die oorspronklike toetsspesifikasies. Die resultate dui daarop dat die ontwerpsparameters vir die NTNKTs by Majuba-kragstasie, ‘n verkoelings-sisteem wat aanvanklik optimaal ontwerp is, op ‘n ander, selfs meer akkurate manier bepaal kon word deur die natbol-temperatuur (Tawb) te gebruik as die hoof-ontwerpsparameter inplaas van die droëbol temperatuur (Ta).’n Nuwe tegniek wat gebruik kan word om akkurate NTNKT ontwerp- en werkverrigting toetsspesifikasies te bepaal word voorgestel. Die tydperk vir die mees optimale atmosferiese toestande, wanneer NTNKT-toetse uitgevoer moet word, word vasgestel as tussen 12:00 en 14:00 tydens Somermaande. Dit word bewys, vir ’n Tawb akkuraatheid van 0.1 K, dat die NTNKT inlaat-Tawb, gemeet by verskillende hoogtes, nie vergelykbaar is met Tawb wat ver van die NTNKT af op dieselfde hoogtes gemeet word nie. ’n Meer aanvaarbare hoogte van 10 m word voorgestel as die NTNKT ontwerpstemperatuur verwysingshoogte vir toekomstige NTNKT ontwerpe wanneer die Tawb ver van die NTNKT af meet word. Die industrie-standaard temperatuur verwysingshoogte moet wel steeds gebruik word tydens temperatuur-profielberekeninge. ’n Parametriese studie van die turbine se water-stoom siklus en die nat-verkoelingstelsel by Majuba dui daarop dat die generator se uitset (Pst) hoofsaaklik afhanklik is van die kondensator se druk (pc) gedurende vol-vrag toestande. Druk (pc) is weer afhanklik van Tawb, die temperatuur vervaltempo (LRT) wat voorgestel word deur die temperatuur profiel eksponent (bT), die verkoelingswater-vloeitempo (mcw), atmosferiese druk (pa) en windspoed (VW). Deur die gebruik van historiese data word redelike eenvoudige metodes voorgestel om dié verhoudings doeltreffend te bepaal. Die atmosferiese- en stasie-spesifieke parameters wat benodig word vir dié ontleding is ook getabuleer. Twee modelle vir NTNKT-effektiweit, ’n wiskundige (gebaseer op Kröger, 1998) en statistiese kunsmatige neurale-netwerk (KNN) model, word aangebied en geëvalueer. KNNe, wat nie gereeld gebruik word om NTNKTe se effektiwiteit te evalueer nie, lewer akkurate NTNKT temperatuur-benadering resultate binne 0.5 K van die gemete resultate vir wisselende afhanklike parameters. Dié resultate motiveer dat ’n KNN wat korrek opgestel is doeltreffend gebruik kan word om die toestand van NTNKTs te bepaal en om die akkuraatheid van ander NTNKT-modelle te verbeter. Die eendimensionele, wiskundige model lewer akkurate resultate onder NTNKT ontwerpspesifikasies. ’n Wiskundige NTNKT-model word gebruik om die afhanklikheid van Majubakragstasie se NTNKTe tot die reënsone druppelgrootte (dd) te bereken. 'n Vermindering in dd van 0,0052 tot 0,0029 m kan die NTNKT se afgekoelde watertemperatuur (Tcwo), van só 'n aard verlaag dat pc verminder met 0,15 kPa. Só kan ’n gesamentlike vol- en gedeeltelike vrag finansiële besparing van R1.576M in 2013 en R1.851M in 2016 behaal word. Soortgelyke verbeterings aan verkoelingstelsels sal lei tot meer en hoër besparings by ander Eskom nat-verkoelde stasies. Dié tegnieke moet in ag geneem word tydens toekomstige ekonomiese evaluasies van verbeterings tot nat-verkoelingstelsels by ander kragstasies.

本篇論文要探討的主題為何種總體或個體因素會影響投保人在壽險上的解約行為。由於壽險保單的解約行為會讓保險公司面臨現金流、聲譽、逆選擇等風險，進而影響公司營運。因此探討影響保單解約率之因素，進而準確估計保單的解約率為十分重要的議題。此外，不論投保人主動解約或是被動使保單失效均會對保險公司造成影響，因此本篇論文也將利用不同解約率的計算方式進行實證分析，研究是否不同計算方式的解約率會影響實證結果。本文使用NAIC (National Association of Insurance Commissioners)保險資料庫之年報資料，對2004-2014年間保險公司之經營狀況進行分析，驗證解約率實證中常用的三個假說：市場利率假說、緊急資金假說以及保單替換假說，選用之變數包含失業率、利率、保單替換率、高齡比等變數，並採用固定效果模型作為縱橫資料之迴歸模型，分別對不同計算方式所得之解約率進行迴歸分析，並比較彙整其結果。最後針對結果提出未來研究之建議。 / Insurance companies’ business will be influenced by surrender activities in several aspects, such as cash flow problem and inverse selection problem. Empirical researches show that both macroeconomic variables and microeconomic variables will influence surrender behaviors. Hence, this paper seeks to which kinds of macroeconomic variables will influence surrender activities and investigates whether using different ways to calculate surrender rate will cause different empirical results. All available US insurance company data, ranging from January 2004 to December 2014, are obtained from the annual statement in NAIC (National Association of Insurance Commissioners).We found some evidence supporting Emergency Fund Hypothesis and Interest Rate Hypothesis, but using different ways to calculate surrender rate may cause a little bias in conclusion. However, the relationship between surrender activities and macroeconomic variables supports insurance companies to understand and actively manage lapse/surrender risk.

[pt] O tema central deste trabalho é apresentar modelos de persistência. As probabilidades de persistência na carteira de um produto de determinada empresa de seguros e previdência serão estudadas de forma agregada, de tal forma que se torna possível a elaboração de outros estudos, como por exemplo, de análise de lucratividade, mesmo com poucos dados, o que inviabiliza a elaboração de tábuas de múltiplos decrementos. Serão avaliadas as possíveis causas de saídas de acordo com as características do plano. O desenvolvimento dos modelos tomam por base dados em forma de triângulo, técnica normalmente utilizada para cálculo de provisões de seguros. / [en] The objective of this work is to present persistency models. The probabilities of remaining in a Insurance and Pension company portfolio will be studied in a aggregate way, in this way it is possible to develop another results such as profitability, even though, there is poor data, what turns impossible to build multiple decrement tables. The possible lapses causes will be evaluated according to the plan. The models development is based on triangular data, this technique is usual on claims reserving.

本研究以保險事業發展中心之資料分析各種不同因子如年度、性別、保額、有無體檢、保費繳別、保單年度及利差、利率等對脫退率之影響，並將其中較具顯著影響的因子納入脫退率模型之建立，期望能藉此模型準確估計台灣壽險公司生死合險、終身壽險以及定期壽險之脫退率，進而幫助壽險公司之財務規劃。 自本研究之分析發現其中最具影響力之因子為保單生效後之保單年度，因此以此為主軸建立脫退率模型，接著，亦考量利差以及利率所呈現的趨勢於其中分別建立保單年度利差模型以及保單年度利率模型，此外，更完整考量本研究中脫退率相關因素，以羅吉斯迴歸方法建立模型。最後將此四種模型應用於壽險公司準備金之提存，以生死合險為例模擬公司現金流量，發現準備金之分配如同 Tsai et al.(2002)受利率風險影響甚鉅，而加入本研究所建立之四種脫退率模型模擬後，反而減少了公司未來所須面臨的利率風險，其中又以保單年度模型影響最大，而第四種脫退率模型不同於Tsai et al.根據台灣壽險經驗加入所有具影響之因素，其模擬結果介於保單年度模型以及保單年度利率模型間，可發現考量因素之不同對脫退率影響甚鉅，繼而影響準備金之提存。 / In this article, we focus on the causes and the features of lapse rate including year, sex, size, underwriting method, premium payment mode, policy year, interest rate and interest rate difference by collecting and analyzing the empirical data of endowment, whole life insurance and term life insurance in Taiwan from Taiwan Insurance Institute. Then we take factors that have effect with lapse rate into account to establish model, and we hope to accurately estimate the lapse rate of endowment, whole life insurance and term life insurance in Taiwan by these models, and assist the life insurance companies’ financial decision making. After analyzing, we find the most effective factor of this study is the policy year, which means the year after issuing, so we take this one as our primary consideration of our lapse rate model. Then we add the interest rate difference and interest rate in the further two models. Beside this, we further consider the important factors in the part of analysis and put it in the fourth model by using Logistic Regression Model. Finally, we apply these four models to the policy reserve of life insurance company by taking endowment policy as an example simulating the cash flow. We find that the results was same as Tsai et al. (2002) that distribution of policy reserve is strongly affected by interest rate risk, but can decrease interest rate risk the company have to face in the future by adding our lapse rate models, especially the policy year model, and the fourth lapse rate model which count into most factors was not the same as Tsai et al. producing result between policy year model and the policy- interest rate model. From the results of all the lapse rate model. We can know that considering different factors in the model will bring such distinct contribution amount of reserve for life insurance company.

Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: An accurate description of the atmospheric boundary layer (ABL) is a prerequisite for computational fluid dynamic (CFD) wind studies. This includes taking into account the thermal stability of the atmosphere, which can be stable, neutral or unstable, depending on the nature of the surface fluxes of momentum and heat. The diurnal variation between stable and unstable conditions in the Namib Desert interdune was measured and quantified using the wind velocity and temperature profiles that describe the thermally stratified atmosphere, as derived by Monin- Obukhov similarity theory. The implementation of this thermally stratified atmosphere into CFD has been examined in this study by using Reynoldsaveraged Navier-Stokes (RANS) turbulence models. The maintenance of the temperature, velocity and turbulence profiles along an extensive computational domain length was required, while simultaneously allowing for full variation in pressure and density through the ideal gas law. This included the implementation of zero heat transfer from the surface, through the boundary layer, under neutral conditions so that the adiabatic lapse rate could be sustained. Buoyancy effects were included by adding weight to the fluid, leading to the emergence of the hydrostatic pressure field and the resultant density changes expected in the real atmosphere. The CFD model was validated against measured data, from literature, for the flow over a cosine hill in a wind tunnel. The standard k-ε and SST k-ω turbulence models, modified for gravity effects, represented the data most accurately. The flow over an idealised transverse dune immersed in the thermally stratified ABL was also investigated. It was found that the flow recovery was enhanced and re-attachment occurred earlier in unstable conditions, while flow recovery and re-attachment took longer in stable conditions. It was also found that flow acceleration over the crest of the dune was greater under unstable conditions. The effect of the dune on the flow higher up in the atmosphere was also felt at much higher distances for unstable conditions, through enhanced vertical velocities. Under stable conditions, vertical velocities were reduced, and the influence on the flow higher up in the atmosphere was much less than for unstable or neutral conditions. This showed that the assumption of neutral conditions could lead to an incomplete picture of the flow conditions that influence any particular case of interest. / AFRIKAANSE OPSOMMING: 'n Akkurate beskrywing van die atmosferiese grenslaag (ABL) is 'n voorvereiste vir wind studies met berekenings-vloeimeganika (CFD). Dit sluit in die inagneming van die termiese stabiliteit van die atmosfeer, wat stabiel, neutraal of onstabiel kan wees, afhangende van die aard van die oppervlak vloed van momentum en warmte. Die daaglikse variasie tussen stabiele en onstabiele toestande in die Namib Woestyn interduin is gemeet en gekwantifiseer deur gebruik te maak van die wind snelheid en temperatuur profiele wat die termies gestratifiseerde atmosfeer, soos afgelei deur Monin-Obukhov teorie, beskryf. Die implementering van hierdie termies gestratifiseerde atmosfeer in CFD is in hierdie studie aangespreek deur gebruik te maak van RANS turbulensie modelle. Die handhawing van die temperatuur, snelheid en turbulensie profiele in die lengte van 'n uitgebreide berekenings domein is nodig, en terselfdertyd moet toegelaat word vir volledige variasie in die druk en digtheid, deur die ideale gaswet. Dit sluit in die implementering van zero hitte-oordrag vanaf die grond onder neutrale toestande sodat die adiabatiese vervaltempo volgehou kan word. Drykrag effekte is ingesluit deur die toevoeging van gewig na die vloeistof, wat lei tot die ontwikkeling van die hidrostatiese druk veld, en die gevolglike digtheid veranderinge, wat in die werklike atmosfeer verwag word. Die CFD-model is gevalideer teen gemete data, vanaf die literatuur, vir die vloei oor 'n kosinus heuwel in 'n windtonnel. Die standaard k-ε en SST k-ω turbulensie modelle, met veranderinge vir swaartekrag effekte, het die data mees akkuraat voorgestel. Die vloei oor 'n geïdealiseerde transversale duin gedompel in die termies gestratifiseerde ABL is ook ondersoek. Daar is bevind dat die vloei herstel is versterk en terug-aanhegging het vroeër plaasgevind in onstabiele toestande, terwyl vloei herstel en terug-aanhegging langer gevat het in stabiele toestande. Daar is ook bevind dat vloei versnelling oor die kruin van die duin groter was onder onstabiele toestande. Die effek van die duin op die vloei hoër op in die atmosfeer is ook op hoër afstande onder onstabiele toestande gevoel, deur middel van verhoogte vertikale snelhede. Onder stabiele toestande, is vertikale snelhede verminder, en die invloed op die vloei hoër op in die atmosfeer was veel minder as vir onstabiel of neutrale toestande. Dit het getoon dat die aanname van neutrale toestande kan lei tot 'n onvolledige beeld van die vloei toestande wat 'n invloed op 'n bepaalde geval kan hê.

Land ice is losing mass to the worlds oceans at an accelerated rate. The worlds glaciers contain much less ice than the ice sheets but contribute equally to eustatic sea level rise and are expected to continue to do so over the coming centuries if global temperatures continue to rise. It is therefore important to characterize the mass balance of these glaciers and its relationship to climate trends and variability. In the Canadian High Arctic, analysis of long-term surface mass balance records shows a shift to more negative mass balances after 1987 and is coincident with a change in the mean location of the July circumpolar vortex, a mid-troposphere cyclonic feature known to have a strong influence on Arctic summer climate. Since 1987 the occurrence of July vortices centered in the Eastern Hemisphere have increased significantly. This change is associated with an increased frequency of tropospheric ridging over the Canadian High Arctic, higher surface air temperatures, and more negative glacier mass balance. However, regional scale mass balance modeling is needed to determine whether or not the long-term mass balance measurements in this region accurately reflect the mass balance of the entire Canadian High Arctic. The Canadian High Arctic is characterized by high relief and complex terrain that result in steep horizontal gradients in surface mass balance, which can only be resolved if models are run at high spatial resolutions. For such runs, models often require input fields such as air temperature that are derived by downscaling of output from climate models or reanalyses. Downscaling is often performed using a specified relationship between temperature and elevation (a lapse rate). Although a constant lapse rate is often assumed, this is not well justified by observations. To improve upon this assumption, near-surface temperature lapse rates during the summer ablation season were derived from surface measurements on 4 Arctic glaciers. Near-surface lapse rates vary systematically with free-air temperatures and are less steep than the free-air lapse rates that have often been used in mass balance modeling. Available observations were used to derive a new variable temperature downscaling method based on temperature dependent daily lapse rates. This method was implemented in a temperature index mass balance model, and results were compared with those derived from a constant linear lapse rate. Compared with other approaches, model estimates of surface mass balance fit observations much better when variable, temperature dependent lapse rates are used. To better account for glacier-climate feedbacks within mass balance models, more physically explicit representations of snow and ice processes must be used. Since absorption of shortwave radiation is often the single largest source of energy for melt, one of the most important parameters to model correctly is surface albedo. To move beyond the limitations of empirical snow and ice albedo parameterizations often used in surface mass balance models, a computationally simple, theoretically-based parameterization for snow and ice albedo was developed. Unlike previous parameterizations, it provides a single set of equations for the estimation of both snow and ice albedo. The parameterization also produces accurate results for a much wider range of snow, ice, and atmospheric conditions.

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